GIFT  OF 

*     Of  A 


LESSONS   IN  ASTRONOMY 

INCLUDING   URANOGRAPHY 

A   BRIEF  INTRODUCTORY   COURSE 
WITHOUT  MATHEMATICS 


BY 

CHARLES  A.  YOUNG,  PH.D.,  LL.D. 

LATE  PROFESSOR  OF  ASTRONOMY  IN  PRINCETON  UNIVERSITY,  AUTHOR 

OF  A  "GENERAL  ASTRONOMY  FOR  COLLEGES  AND  SCIENTIFIC 

SCHOOLS,"  OF  A  "MANUAL  OF  ASTRONOMY,"  AND 

OF  "ELEMENTS  OF  ASTRONOMY" 


REVISED  EDITION 
WITH  ADDITIONS  AND   CORRECTIONS 


GINN  AND  COMPANY 

BOSTON     •     NEW    YORK     •     CHICAGO     •     LONDON 
ATLANTA     •     DALLAS     •     COLUMBUS     •     SAN    FRANCISCO 


ENTERED  AT  STATIONERS1  HALL 


COPYRIGHT,  1891,  1903,  BY 
CHARLES  A.  YOUNG 


COPYRIGHT,  1918,  BY 
G1NN  AND  COMPANY 


ALL  RIGHTS   RESERVED 
A622.ll 


i    - 


ct 


Cfte 


G1NN  AND  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


PREFACE  TO   THE  ORIGINAL  EDITION 


THIS  volume  has  been  prepare4  to  meet  the  want  of 
certain  classes  of  schools  which  find  the  author's  "  Elements 
of  Astronomy  "  rather  too  extended  and  mathematical  to 
suit  their  course  and  pupils.  It  is  based  upon  the  Ele- 
ments, but  with  many  condensations,  simplifications,  and 
changes  of  arrangement:  everything  has  been  carefully 
worked  over  and  rewritten  in  order  to  adapt  it  to  those 
whose  mathematical  attainments  are  not  sufficient  to  enable 
them  to  use  the  larger  work  to  advantage. 

Of  course,  such  pupils  cannot  gain  the  same  insight  into 
the  mechanism  of  the  heavens  as  those  who  take  up  the 
subject  at  a  more  advanced  stage  in  their  education.  They 
must  often  be  contented  with  the  bare  statement  of  a  fact 
without  any  explanation  of  the  manner  in  which  its  truth 
is  established,  and  thus  will  necessarily  miss  much  that  is 
most  valuable  in  the  discipline  to  be  derived  from  the  study 
of  Astronomy. 

But  enough  remains  —  surely  there  is  no  other  science 
which,  apart  from  all  questions  of  How  or  Why,  supplies 
so  much  to  widen  the  student's  range  of  thought  and  to 
make  him  comprehend  his  place  in  the  infinite  universe. 

The  most  important  change  in  the  arrangement  of  the 
book  has  been  in  bringing  the  Uranography,  or  "  constella- 
tion-tracing," into  the  body  of  the  text  and  placing  it  near 

iii 


iv  PREFACE 

the  beginning,  —  a  change  in  harmony  with  the  accepted 
principle  that  those  whose  minds  are  not  mature  succeed 
best  in  the  study  of  a  new  subject  by  beginning  with  what 
is  concrete  and  appeals  to  the  senses,  rather  than  with  the 
abstract  principles.  It  has  been  thought  well  also  to  add 
brief  notes  on  the  legendary  mythology  of  the  constellations 
for  the  benefit  of  such  pupils  as  are  not  likely  to  become 
familiar  with  it  in  the  study  of  classical  literature. 

In  the  preparation  of  the  book  great  pains  have  been 
taken  not  to  sacrifice  accuracy  and  truth  to  compactness, 
and  no  less  to  bring  everything  thoroughly  down  to  date. 

The  Appendix  contains  in  its  first  chapter  descrip- 
tions of  the  most  used  astronomical  instruments,  and  where 
time  permits,  might  profitably  be  brought  into  the  course. 
The  second  chapter  of  the  Appendix  is  designed  only 
for  the  use  of  teachers  and  the  more  advanced  pupils. 
Sees.  431-434,  however,  explaining  how  the  sun's  dis- 
tance may  be  found  in  the  simplest  way,  might  well  be 
read  by  all. 


1891. 


PREFACE   TO    THE   REVISED   EDITION 

SINCE  the  original  publication  of  this  work  twelve  years 
ago,  a  number  of  editions  have  been  issued  in  which  it  was 
attempted  to  keep  up  to  date,  as  far  as  possible,  by  such 
minor  changes  and  corrections  as  typographical  considera- 
tions would  permit.  It  has  now,  however,  seemed  best  to 
reprint  the  book  from  entirely  new  plates,  and  this  has 
given  an  opportunity  for  a  thorough  revision  of  the  work 
and  the  free  introduction  of  all  desirable  improvements 
and  additions.  The  former  rather  unsatisfactory  star-maps 
have  been  replaced  by  new  ones,  and  a  considerable  number 
of  beautiful  half-tone  illustrations  have  been  added. 

The  publishers  have  spared  no  pains  or  expense  in  the 
mechanical  execution  of  the  volume,  and  it  is  hoped  that, 
so  far  as  its  scope  permits,  the  book  will  now  be  found 
to  offer  a  satisfactory  summary  of  the  present  state  of 
Astronomy. 

C.  A.  YOUNG. 
PRINCETON,  N.J., 
January,  1903. 


PREFACE  TO  ISSUE  OF  1918 

WHILE  the  greater  part  of  the  text  remains  as  it  was 
written  by  its  author,  such  changes  have  been  made  in 
this  issue  as  are  necessary  to  bring  it  down  to  date. 

ANNE  SEWELL  YOUNG. 
MOUNT  HOLYOKB  COLLEGE, 
October,  1917. 


CONTENTS 


CHAPTER  I.  —  INTRODUCTION  —  Fundamental  Notions 
and  Definitions  —  The  Celestial  Sphere  and  its  Circles 

—  Altitude  and  Azimuth  —  Right  Ascension  and  Dec- 
imation—  Celestial  Latitude  and  Longitude        .         .         1-19 

CHAPTER  II.  —  URANOGRAPHY  —  Globes  and  Star-Maps 

—  Star   Magnitudes  —  Names    and    Designations    of 

Stars  — The  Constellations  in  Detail  .         .         .         .       20-63 

CHAPTER  III.  —  FUNDAMENTAL  PROBLEMS  —  Latitude 
and  the  Aspect  of  the  Celestial  Sphere  —  Time,  Lon- 
gitude, and  the  Place  of  a  Heavenly  Body  .  .  .  64-77 

CHAPTER  IV.  — THE  EARTH  — Its  Form  and  Dimen- 
sions; its  Rotation,  Mass,  and  Density  —  Its  Orbital 
Motion  and  the  Seasons  —  Precession  —  The  Year  and 
the  Calendar  .  .  ....  .  .  .  78-104 

CHAPTER  V.  — THE  MOON  — Her  Orbital  Motion  and 
the  Month  —  Distance,  Dimensions,  Mass,  Density,  and 
Force  of  Gravity  —  Rotation  and  Librations  —  Phases 

—  Light  and  Heat  —  Physical  Condition  —  Telescopic 
Aspect  and  Surface      .         .         .         ......  105-128 

CHAPTER  VI.  — THE  SUN  — Its  Distance,  Dimensions, 
Mass,  and  Density  —  Its  Rotation,  Surface,  and  Spots 

—  The   Spectroscope  and  the  Solar  Spectrum  —  The 
Chemical  Constitution  of  the  Sun  —  The  Chromosphere 
and  Prominences  —  The  Corona  —  The  Sun's   Light 

—  Measurement  and  Intensity  of  the  Sun's  Heat  — 
Theory  of  its  Maintenance  and  Speculations  regarding 

the  Age  and  Duration  of  the  Sun         ....  129-170 

vii 


viii  CONTENTS 

PAGES 

CHAPTER  VII.  —  ECLIPSES  AND  THE  TIDES  —  Form  and 
Dimensions  of  Shadows  —  Eclipses  of  the  Moon  — 
Solar  Eclipses,  Total,  Annular,  and  Partial  —  Number 
of  Eclipses  in  a  Year  —  Recurrence  of  Eclipses  and 
the  Saros  —  Occupations  —  The  Tides  .  ._  .171-187 

CHAPTER  VIII.  —  THE  PLANETARY  SYSTEM  —  The  Plan- 
ets in  General  —  Their  Number,  Classification,  and 
Arrangement  —  Bode's  Law  —  Orbits  of  the  Planets 

—  Kepler's   Laws    and    Gravitation  —  The    Apparent 
Motions  of  the  Planets  and  the  Systems  of  Ptolemy 
and  Copernicus  —  Determination  of  the  Planets'  Diam- 
eters, Masses,    etc.  —  Herschel's    Illustration    of    the 
System  —  Description    of    Individual    Planets  —  The 

<  Terrestrial '  Planets,  Mercury,  Venus,  and  Mars         .  188-224 

CHAPTER  IX.  —  PLANETS  (Continued )  —  The  Asteroids 

—  Intramercurian  Planets  and  the  Zodiacal  Light  — 
The    Major    Planets,    Jupiter,    Saturn,    Uranus,   and 
Neptune  —  Ultra-Neptunian  Planet     .         .      4.         .225-251 

CHAPTER  X.  —  COMETS  AND  METEORS  —  Comets,  their 
Number,  Designation,  and  Orbits  —  Their  Constituent 
Parts  and  Appearance  —  Their  Spectra,  Physical  Con- 
stitution, and  Probable  Origin  —  Remarkable  Comets 

—  Photography  of  Cornets  —  Aerolites,  their  Fall  and 
Characteristics  —  Shooting-Stars  and  Meteoric  Showers 

—  Connection  between  Meteors  and  Comets         .         .  252-293 

CHAPTER  XI.  — THE  STARS  — Their  Nature,  Number, 
and  Designation  —  Star-Catalogues  and  Charts  —  Their 
Proper  Motions  and  the  Motion  of  the  Sun  in  Space 

—  Stellar  Parallax  —  Star  Magnitudes  and  Photometry 

—  Variable  Stars  —  Stellar  Spectra      ,:      .         .         .294-325 

CHAPTER  XII.  — THE  STARS  (Continued)  —  Double  and 
Multiple  Stars  —  Clusters  and  Nebulae  —  The  Milky 
Way  and  Distribution  of  Stars  in  Space  —  The  Stellar 
Universe  —  Cosmogony  and  the  Nebular  Hypothesis  ,  326-357 


CONTENTS  ix 

APPENDIX 

PAGES 

ASTRONOMICAL  INSTRUMENTS.  —  The  Telescope, 
Simple  Refracting,  Achromatic,  and  Reflecting  —  The 
Equatorial  —  The  Filar  Micrometer  —  The  Transit- 
Instrument  —  The  Clock  and  the  Chronograph  —  The 
Meridian  Circle  —  The  Sextant  .  .  .  .  ..  .359-378 

MISCELLANEOUS  (FOR  THE  MOST  PART  SUPPLEMEN- 
TARY TO  ARTICLES  IN  THE  TEXT).  —  Hour- Angle  and 
Time  —  Twilight  —  Determination  of  Latitude  —  Place 
of  a  Ship  at  Sea  —  Finding  the  Form  of  the  Earth's 
Orbit  —  The  Ellipse  —  Illustrations  of  Kepler's  "  Har- 
monic "  Law  —  The  Equation  of  Light  and  the  Sun's 
Distance  determined  by  it  —  Aberration  of  Light  — 
De  1'Isle's  Method  of  getting  the  Sun's  Parallax  from  a 
Transit  of  Venus  —  The  Parabola  and  the  Conic  Sec- 
tions—  Determination  of  Stellar  Parallax  .  .  .378-397 

QUESTIONS  FOR  REVIEW  .        .         .        .        .        .398-400 

TABLES  OF  ASTRONOMICAL  DATA 

I.  Astronomical  Constants      -«_.:•     .         «        V  .  401 

II.  The  Principal  Elements  of  the  Solar  System  .  402 

III.  The  Satellites  of  the  Solar  System        .         .  .  403 

IV.  The  Principal  Variable  Stars        .         .         .  .  404 
V.  The  Best  Determined  Stellar  Parallaxes        .  .  405 

The  Greek  Alphabet  and  Miscellaneous  Symbols  .  406 

INDEX      .         .         .         .       . .         .         .  __.;.,,.        .         .  407-420 

STAR-MAPS 


LESSONS  IN  ASTRONOMY 


CHAPTER   I 
INTRODUCTION 

Fundamental  Notions  and  Definitions  —  The  Celestial  Sphere  and  its  Circles 
—  Altitude  and  Azimuth  —  Right  Ascension  and  Declination  —  Celestial 
Latitude  and  Longitude 

1.  Astronomy1  is  the  science  which  deals  with  the 
heavenly  bodies. 

As  it  is  the  oldest  of  the  sciences,  so  also  it  is  one  of  the 
most  perfect,  and  in  certain  aspects  the  noblest,  as  being 
the  most  "  unselfish  "  of  them  all.  And  yet,  although  not 
bearing  so  directly  upon  the  material  interests  of  life  as 
the  more  modern  sciences  of  Physics  and  Chemistry,  it  is 
of  high  utility. 

By  means  of  Astronomy  the  latitudes  and  longitudes  of 
places  upon  the  earth's  suface  are  determined,  and  by  such 
determinations  alone  is  navigation  made  secure.  More- 
over, all  the  operations  of  surveying  upon  a  large  scale, 
such  as  the  determination  of  national  boundaries,  depend 
more  or  less  upon  astronomical  observations.  The  same 
is  true  of  operations  which,  like  the  railway  service,  require 
an  accurate  knowledge  and  observance  of  time ;  for  the 
fundamental  timekeeper  is  the  diurnal  revolution  of  the 
heavens. 

1  The  term  is  derived  from  two  Greek  words :  astron  (a  heavenly  body) 
and  noinos  (a  law). 

1 


2  LESSONS  IN  ASTRONOMY 

In  ancient  times  the  science  was  supposed  to  have  a  still  higher 
utility.  It  was  believed  that  human  affairs  of  every  kind,  the  wel- 
fare of  nations,  and  the  life  history  of  individuals  alike,  were  con- 
trolled, or  at  least  prefigured,  by  the  motions  of  the  stars  and  planets  ; 
so  that  from  the  study  of  the  heavens  it  ought  to  be  possible  to  pre- 
dict futurity.  Hence  originated  the  pseudo-science  of  Astrology, 
which,  baseless  and  absurd  as  it  has  been  proved  to  be,  still  retains 
a  remarkable  hold  on  the  popular  mind. 

2.  The  heavenly  bodies  include,  first,  the  solar  system, 
—  that  is,  the  sun  and  the  planets  which  revolve  around 

it,  with  their  attendant  satellites;  second,  the  comets  and 
the  meteors,  which  also  move  around  the  sun,  but  are 
bodies  of  a  very  different  nature  from  the  planets  and 
travel  in  different  orbits ;  and,  third,  the  stars  and  nebulse. 
The  earth  on  which  we  live  is  one  of  the  planets,  and 
the  moon  is  the  earth's  satellite.  The  stars  which  we  see 
are  bodies  of  the  same  kind  as  the  sun,  shining  like  him 
with  fiery  heat,  while  the  planets  and  the  satellites  are 
dark  and  cool  like  the  earth  and  visible  only  by  the  sun- 
light they  reflect.  As  for  the  comets  and  nebulae,  they 
appear  to  be  mere  clouds,  composed  of  gas  or  swarms 
of  little  particles,  perhaps  not  very  hot,  but  luminous. 
It  is  likely,  practically  certain  indeed,  that  besides  the 
visible  stars  there  are  also  multitudes  of  others  too  cool 
to  shine,  some  of  winch  manifest  their  existence  by 
affecting  the  motion  of  certain  of  the  visible  stars.  It  is 
hardly  necessary  to  add  that  while  with  the  naked  eye 
we  see  only  a  few  thousand  stars,  the  telescope  reveals 
millions. 

3.  As  we  look  off  from  the  earth  at  night,  the  stars 
appear  to  be  all  around  us,  like  glittering  points  fastened 
to  the  inside  of  a  huge  hollow  globe.     Really  they  are  at 


INTRODUCTION  3 

very  different  distances,  all  enormous  as  compared  with 
any  distances  with  which  geography  makes  us  familiar. 
Even  the  moon  is  eighty  times  as  far  away  as  New  York 
from  Liverpool,  and  the  sun  is  nearly  four  hundred  times 
as  distant  as  the  moon,  and  the  nearest  of  the  stars  is 
nearly  three  hundred  thousand  times  as  distant  as  the  sun ; 
as  to  the  remoter  stars,  some  of  them  are  certainly  thou- 
sands of  times  as  far  away  as  the  nearer  ones,  —  so  far 
that  light  itself  is  thousands  of  years  in  coming  to  us  from 
them.  These  are  facts  which  are  certain,  not  mere  guesses 
or  beliefs. 

Then,  too,  as  to  their  motions.  Although  most  of  the 
heavenly  bodies  seem  to  us  to  be  at  rest,  except  as  the 
earth's  rotation  makes  them  appear  to  rise  and  set,  yet 
really  they  are  all  moving,  and  with  a  swiftness  of  which 
we  can  form  no  conception.  A  cannon-ball  is  a  snail  com- 
pared with  the  slowest  of  them.  The  earth  itself  in  its 
revolution  around  the  sun  is  flying  eighteen  and  a  half 
miles  in  a  second,  which  is  more  than  fifty  times  as  fast  as 
the  swiftest  rifle  bullet.  We  fail  to  perceive  the  motion 
simply  because  it  is  so  smooth  and  so  unresisted.  The 
space  outside  our  air  contains  nothing  that  obviously 
obstructs  either  sight  or  motion. 

4.  But  this  knowledge  as  to  the  real  distance  and 
motions  of  the  heavenly  bodies  was  gained  only  after 
long  centuries  of  study.  If  we  go  out  to  look  at  the  stars 
some  moonless  night,  we  find  them  apparently  sprinkled 
over  the  dome  of  the  sky  in  groups,  or  constellations,  which 
are  still  substantially  the  same  as  in  the  days  of  the  earliest 
astronomers.  At  first  these  constellations  were  figures  of 
animals  and  other  objects,  and  many  celestial  globes  and 


4  LESSONS  IN  ASTRONOMY 

maps  still  bear  grotesque  pictures1  representing  them.  At 
present,  however,  a  constellation  is  only  a  certain  region 
of  the  sky,  limited  by  imaginary  lines  which  divide  it 
from  the  neighboring  constellations,  just  as  countries  are 
divided  in  geography.  As  to  the  exact  boundaries  of  these 
constellations,  and  even  their  number,  there  is  no  precise 
agreement  among  astronomers.  Forty-eight  of  them  have 
come  down  to  us  from  the  time  of  Ptolemy  (the  greatest 
astronomer  of  antiquity,  who  flourished  at  Alexandria  about 
A.D.  130),  and  even  in  his  day  many  of  them  were  already 
ancient. 

About  twenty  others,  proposed  by  later  astronomers,  are 
now  generally  recognized,  and  at  least  as  many  more  have 
been  suggested  and  abandoned. 

5.  Uranography,  or  Description  of  the  Visible  Heavens.  — 
The  study  of  the  constellations,  or  the  apparent  arrange- 
ment of  the  stars  in  the  sky,  is  called  Uranography.2  It 
is  not  an  essential  part  of  Astronomy,  but  it  is  an  easy  and 
pleasant  study;  and  in  becoming  familiar  with  the  con- 
stellations and  their  principal  stars  the  pupil  will  learn 
more  readily  and  thoroughly  than  in  any  other  way  the 
most  important  facts  in  relation  to  the  apparent  motions 
of  the  heavenly  bodies,  and  the  principal  points  and 
circles  of  the  celestial  sphere.  For  this  reason  the  teacher 
is  urged  to  take  the  earliest  opportunity  to  have  his 
pupils  trace  such  of  the  constellations  as  happen  to  be 
visible  in  the  evening  sky  when  they  begin  the  study  of 
Astronomy,  and  to  continue  it  from  time  to  time  as  the 
progress  of  the  seasons  gives  opportunity. 

1  Most  of  these  figures  follow  the  designs  of  Albert  Diirer. 

a  From  the  Greek,  ouranos  (heavens)  and  grapM  (description). 


INTRODUCTION  5 

6.  The  Celestial  Sphere.1  —  The  sky  appears  like  a  hollow 
vault,  to  which  the  stars  seem  to  be  attached  like  specks 
of  gilding  upon  the  inner  surface  of  a  dome.     We  cannot 
judge  of  the  distance  of  this  surface  from  the  eye,  further 
than  to  perceive  that  it  must  be  very  far  away.    It  is  there- 
fore natural  and  extremely  convenient  to  regard  the  dis- 
tance of  the  sky  as  everywhere  the  same  and  unlimited. 
The  celestial  sphere,  as  it  is  called,  is  conceived  of  as  so 
enormous  that  the  whole  world  of  stars  and  planets  lies 
in  its  center  like  a  few  grains  of  sand  in  the  middle  of 
the  dome  of  the  Capitol.     Its  diameter  is  assumed  to  be 
immeasurably  greater   than   any  actual   distance    known, 
and  greater  than  any  quantity  assignable.     In  technical 
language  it  is  taken  as  infinite. 

Since  the  celestial  sphere  is  thus  infinite,  any  two 
parallel  lines  drawn  from  distant  points  on  the  surface  of 
the  earth,  or  even  from  points  as  distant  as  the  earth  and 
the  sun,  will  seem  to  meet  at  one  point  on  the  surface  of  the 
sphere.  If  the  two  lines  were  anywhere  a  million  miles 
apart,  for  instance,  they  will,  of  course,  still  be  a  million 
miles  apart  when  they  reach  the  surface  of  the  sphere; 
but  at  an  infinite  distance  even  a  million  miles  is  a  mere 
nothing,  so  that,  to  our  observation,  the  two  lines  are  close 
together  and  make  apparently  but  a  single  point2  where 
they  pierce  the  sphere. 

7.  The  Apparent  Place  of  a  Heavenly  Body.  —  This  is 
simply  the  point  where  a  line  drawn  from  the  observer 

1  The  study  of  the  celestial  sphere  and  its  circles  is  greatly  facilitated 
by  the  use  of  a  globe,  or  armillary  sphere.    Without  some  such  apparatus 
it  is  not  easy  for  a  young  person  to  get  clear  ideas  upon  the  subject. 

2  This  is  the  same  as  the  "vanishing  point "  of  perspective. 


LESSONS  IN  ASTRONOMY 


through  the  body  in  question,  continued  outward,  pierces 
the  celestial  sphere.  It  depends  solely  upon  the  direction 
of  the  body,  and  is  in  no  way  affected  by  its  distance  from 
us.  Thus,  in  Fig.  1,  A,  B,  C,  etc.,  are  the  apparent  places 
of  a,  b,  c,  etc.,  the  observer  being  at  0.  Objects  that  are 
nearly  in  line  with  each  other,  however  great  the  real  dis- 
tances between  them,  as  h,  i,  k,  will  appear  close  together 
in  the  sky.  The  moon,  for  instance,  often  looks  to  us 

uvery  near"  a  star,  which 
is  really  of  course  at  an 
enormous  distance  beyond 
her. 

8.  Angular  Measurement. 
—  It  is  clear  that  we  cannot 
properly  describe  the  appar- 
ent distance  of-  two  points 
upon  the  celestial  sphere  from 
each  other  by  feet  or  inches. 
To  say  that  two  stars  are 
about  five  feet  apart,  for  in- 
stance,—  and  it  is  not  very  uncommon  to  hear  such  an 
expression,  —  means  nothing  unless  we  know  how  far  from 
the  eye  the  five-foot  measure  is  to  be  held.  The  proper 
units  for  expressing  apparent  distance  in  the  sky  are  those 
of  angle,  viz. :  degrees  (°),  minutes  ('),  and  seconds  (") ;  the 
circumference  of  a  circle  being  divided  into  360  degrees, 
each  degree  into  60  minutes,  and  each  minute  into  60 
seconds.  Thus,  the  Great  Bear's  tail,  or  "  Dipper-handle," 
is  about  16°  long,  and  the  long  side  of  the  "  Dipper-bowl " 
is  about  10°;  the  moon  and  the  sun  are  each  about  half  a 
degree,  or  30',  in  diameter. 


FIG.  1 


INTRODUCTION  7 

It  is  very  important  that  the  student  in  Astronomy  should  become 
accustomed  as  soon  as  possible  to  estimate  celestial  measures  in  this 
way.  A  little  practice  soon  makes  it  easy,  though  at  first  one  is  apt 
to  be  embarrassed  by  the  fact  that  the  sky  looks  to  the  eye  not  like 
a  true  hemisphere  but  like  a  flattened  vault,  so  that  the  estimates  of 
distances  for  all  objects  near  the  horizon  are  apt  to  be  too  large. 
The  moon,  when  rising  or  setting,  looks  to  most  persons  much  larger 
than  when  overhead ; x  and  the  Dipper-bowl,  when  underneath  the 
pole,  seems  to  cover  a  much  larger  area  than  when  above  it. 

9.  Circles  and  Principal  Points  of  the  Celestial  Sphere.  — 

Just  as  the  surface  of  the  earth  in  Geography  is  covered 
with  a  network  of  imaginary  lines,  —  meridians  and  par- 
allels of  latitude,  —  so  the  sky  is  supposed  to  be  marked 
off  in  a  somewhat  similar  way.  Two  such  sets  of  points 
and  reference  circles  are  in  common  use  to  describe  the 
apparent  places  of  the  stars,  and  a  third  was  used  by  the 
ancients  and  is  still  employed  for  some  purposes.  The  first 
system  depends  upon  the  direction  of  the  force  of  gravity 
shown  by  a  plumb-line  at  the  point  where  the  observer 
stands ;  the  second  upon  the  direction  of  the  axis  of  the 
earth,  which  points  very  near  to  the  so-called  Pole-star; 
and  the  third  depends  upon  the  position  of  the  orbit  in 
which  the  earth  travels  around  the  sun. 

10.  The  Gravitational  or  Up-and-Down  System. — (a)  The 
Zenith  and  Nadir.     The  point  in  the  sky  directly  above 
the  observer  is  called  the  zenith;  the  opposite  point,  under 
the  earth  and  of  course  invisible,  the  nadir? 

1  This  is  a  pure  illusion  due  to  physiological  causes  affecting  judg- 
ment of  distance  and  size.     The  moon  at  the  horizon  is  really  about 
4000  miles  more  distant  from  the  observer  than  when  nearly  overhead, 
and  its  apparent  diameter,  as  measured  by  an  astronomical  instrument,  is 
actually  less  by  about  one-thirtieth. 

2  These  are  Arabic  terms.    About  A.D.  1100  the  Arabs  were  the  world's 


g  LESSONS  IN  ASTRONOMY 

(b)  The  Horizon  (pronounced  ho-ri'-zon,  not  hor'-i-zon). 
This  is  a  "great  circle  '^around  the  sky,  half-way  between 
the  zenith  and  the  nadir,  and  therefore  everywhere  90° 
from  the  zenith.  The  word  is  derived  from  a  Greek  word 
which  means  a  "boundary";  i.e.,  the  line  where  the  earth 
or  sea  limits  the  sky.  The  actual  line  of  division,  which 
on  the  land  is  always  more  or  less  irregular,  is  called  the 
visible  horizon,  to  distinguish  it  from  the  true,  or  astro- 
nomical, horizon  denned  above. 

We  may  also  define  the  horizon  as  the  great  circle  where 
a  plane  which  passes  through  the  observer's  eye  perpen- 
dicular to  the  plumb-line  cuts  the  celestial  sphere. 

11.  Vertical  Circles  and  the  Meridian ;  Altitude  and  Azi- 
muth. —  Circles  drawn  from  the  zenith  to  the  nadir  cut  the 
horizon  at  right  angles,  and  are  known  as  vertical  circles. 
Each  star  has  at  any  moment  its  own  vertical  circle. 

That  particular  vertical  circle  which  passes  north  and 
south  is  known  as  the  Celestial  Meridian ;  while  the  ver- 
tical circle  at  right  angles  to  this  is  called  the  prime  vertical. 
Small  circles  drawn  parallel  to  the  horizon  are  known  as 
parallels  of  altitude,  or  almucantars.  Fig.  2  illustrates  these 
definitions. 

By  their  help  we  can  easily  define  the  apparent  position 
of  a  heavenly  body. 

Its  Altitude  is  its  apparent  elevation  above  the  horizon ; 
that  is,  the  number  of  degrees  between  it  and  the  horizon, 
measured  on  a  vertical  circle.  Thus,  in  Fig.  2,  the 

chief  astronomers,  and  have  left  their  mark  upon  the  science  in  numerous 
names  of  stars  and  astronomical  terms. 

1  "Great  Circles"  are  those  which  divide  the  sphere  into  two  equal 
parts. 


INTRODUCTION 


9 


vertical  circle  ZMH  passes  through  the  point  M.  The  arc 
MH,  measured  in  degrees,  is  the  altitude  of  M,  and  the 
arc  ZM  is  called  its  zenith  distance. 

The  Azimuth  of  a  heavenly  body  is  the  same  as  its 
"  bearing "  in  Surveying,  but  measured  from  the  true 
meridian  and  not  from  the  magnetic.1  It  is  the  arc  of 
the  horizon,  measured  in  degrees,  intercepted  between  the 


FIG.  2.  —  The  Horizon  and  Vertical  Circles 


O,  the  place  of  the  observer. 
OZ,  the  observer's  vertical. 
Z,  the  zenith  ;  P,  the  pole. 
SWNE,  the  horizon. 
SZPN,  the  meridian. 
EZW,  the  prime  vertical. 


M,  some  star. 

ZMH,  arc  of  the  star's  vertical  circle. 

TMR,  the  star's  almucantar. 

Angle  TZM,  or  arc  SH,  star's  azimuth. 

Arc  HM,  star's  altitude. 

Arc  ZM,  star's  zenith-distance. 


south  point  and  the  foot  of  the  vertical  circle  which  passes 
through  the  object. 

There  are  various  ways  of  reckoning  azimuth.  Many 
writers  express  it  in  the  same  way  as  the  "bearing"  in 
Surveying,  i.e.,  so  many  degrees  east  or  west  of  north  or 
south.  In  the  figure,  the  azimuth  of  M  thus  expressed 
is  about  $,  50°  E.  The  more  usual  way  at  present  is, 

1  The  reader  is  reminded  that  the  magnetic  needle  hardly  anywhere 
points  exactly  north.  Its  direction  varies  widely  at  different  parts  of  the 
earth,  and,  moreover,  is  continually  changing  to  some  extent. 


10  LESSONS  IX  ASTRONOMY 

however,  to  reckon  clear  around  from  the  south,  through 
the  west,  to  the  point  of  beginning.  Expressed  in  this 
way,  the  azimuth  of  M  would  be  about  310°,  —  i.e.,  the 
arc  SWNEH. 

Altitude  and  azimuth,  however,  are  inconvenient  for 
many  purposes,  because  they  continually  change  for  a 
celestial  object  as  it  apparently  moves  across  the  sky. 

12.  The  Apparent  Diurnal  Rotation  of  the  Heavens.  — 
If  we  go  out  on  some  clear  evening  in  the  early  autumn, 
say  about  8  P.M.  on  the  22d  of  September,  and  face  the 
north,  we  shall  find  the  appearance  of  that  part  of  the 
heavens  directly  before  us  substantially  as  shown  in  Fig.  3. 
In  the  north  is  the  constellation  of  the  Great  Bear  (Ursa 
Major),  characterized  by  the  conspicuous  group  of  seven 
stars  known  as  the  "  Great  Dipper."  It  now  lies  with  its 
handle  sloping  upward  to  the  west.  The  two  eastern- 
most stars  of  the  four  which  form  its  bowl  are  called  the 
"  Pointers,"  because  they  point  to  the  Pole-star,  which  is 
a  solitary  star  not  quite  half-way  from  the  horizon  to  the 
zenith  (in  the  latitude  of  New  York),  and  about  as  bright 
as  the  brighter  of  the  two  Pointers. 

High  up  on  the  opposite  side  of  the  Pole-star  from  the 
Great  Dipper,  and  at  nearly  the  same  distance,  is  an 
irregular  zigzag  of  five  stars,  each  about  as  bright  as  the 
Pole-star  itself.  This  is  the  constellation  of  Cassiopeia. 

If  now  we  watch  these  stars  for  only  a  few  hours,  we 
shall  find  that  while  all  the  forms  remain  unaltered,  their 
places  in  the  sky  are  slowly  changing.  The  Great  Dipper 
slides  downward  towards  the  north,  so  that  by  eleven  o'clock 
(on  September  22)  the  Pointers  are  directly  un\der  the 

Pole-star.    Cassiopeia  still  keeps  opposite,  however,  rising 

i 


INTRODUCTION 


11 


towards  the  zenith ;  and  if  we  continue  the  watch  through 
the  whole  night,  we  shall  find  that  all  the  stars  appear  to 
be  moving  in  circles  around  a  point  near  the  Pole-star, 
revolving  in  the  opposite  direction  to  the  hands  of  a  watch 


FIG.  3.  —  The  Northern  Circumpolar  Constellations 

) 

(as  we  look  towards  the  north)  with  a  steady  motion  which 
takes  them  completely  around  once  a  day,  or,  to  be  more 
exact,  once  in  23h56m48.l  of  ordinary  time.  They  behave 


12  LESSONS  IN  ASTRONOMY 

just  as  if  they  were  attached  to  the  inner  surface  of  a  huge 
revolving  sphere. 

Instead  of  watching  the  stars  by  the  eye  we  may  advan- 
tageously employ  photography.  A  camera  is  pointed  up 
towards  the  Pole-star  and  kept  firmly  fixed  while  the  stars 

by  their  diurnal 
motion  impress 
their  "trails"  upon 
the  plate.  Fig.  4 
was  made  in  this 
way  with  an  ex- 
posure of  about 
nine  hours. 

To  indicate  the 
position  of  the  stars 
as  it  will  be  at  mid- 
night of  September  22, 
the  figure  must  be 
held  so  that  XII  in 

FIG.  4.  -Polar  Star  Trails  the  marSin  is  at  the 

bottom ;  at  4  A.M.  the 

stars  will  have  come  to  the  position  indicated  by  bringing  XVI 
to  the  bottom,  and  so  on.  But  at  eight  o'clock  on  the  next  night 
we  shall  find  things  very  nearly  in  their  original  position. 

If  instead  of  looking  toward  the  north  we  now  look 
southward,  we  shall  find  that  in  that  part  of  the  sky  also 
the  stars  appear  to  move  in  the  same  kind  of  way.  All 
that  are  not  too  near  the  Pole-star  rise  somewhere  in  the 
eastern  horizon,  ascend  obliquely  to  the  meridian,  and 
descend  to  their  setting  at  points  on  the  western  horizon. 
The  next  day  they  rise  and  set  again  at  precisely  the  same 
points,  and  the  motion  is  always  in  an  arc  of  a  circle,  called 


INTRODUCTION  13 

the  star's  diurnal  circle,  the  size  of  which  depends  upon  its 
distance  from  the  pole.  Moreover,  all  of  these  arcs  are 
strictly  concentric. 

The  ancients  accounted  for  these  fundamental  and  obvious 
facts  by  supposing  that  the  stars  are  really  fastened  to  the 
celestial  sphere,  and  that  this  sphere  really  turns  daily  in 
the  manner  indicated.  According  to  this  view  there  must 
really  be  upon  the  sphere  two  opposite  points  which  remain 
at  rest,  and  these  are  the  poles. 

13.  Definition  of  the  Poles.  —  The  Poles,  therefore,  may 
be  defined  as  those  two  points  in  the  sky  where  a  star  would 
have  no  diurnal  motion.  The  exact  position  of  either  pole 
may  be  determined  with  proper  instruments  by  finding  the 
center  .of  the  small  diurnal  circle  described  by  some  star 
near  it,  as,  for  instance,  by  the  Pole-star. 

This  definition  of  the  pole  is  that  which  would  be  given 
by  one  familiar  with  the  sky  but  ignorant  of  the  earth's 
rotation,  and  it  is  still  perfectly  correct ;  but  knowing,  as 
we  now  do,  that  this  apparent  revolution  of  the  celestial 
sphere  is  due  to  the  real  spinning  of  the  earth  on  its  axis, 
we  may  also  define  the  poles  as  the  two  points  where  the 
earth's  axis  of  rotation,  produced  indefinitely,  would  pierce 
the  celestial  sphere. 

Since  the  two  poles  are  diametrically  opposite  in  the  sky,  only  one 
of  them  is  usually  visible  from  any  given  place.  Observers  north 
of  the  earth's  equator  see  only  the  north  pole,  and  vice  versa  for 
observers  in  the  southern  hemisphere. 

The  student  must  be  careful  not  to  confound  the  Pole 
with  the  Pole-star.  The  pole  is  an  imaginary  point ;  the 
Pole-star  is  only  that  one  of  the  conspicuous  stars  which 


14 


LESSONS  IN  ASTRONOMY 


happens l  now  to  be  nearest  to  that  point  and  at  present  is 
about  li°  distant  from  it.  If  we  draw  an  imaginary  line 
from  the  Pole-star  to  the  star  Mizar  (the  one  at  the  bend 
of  the  Dipper-handle),  it  will  pass  almost  exactly  through 
the  pole  itself ;  the  distance  of  the  pole  from  the  Pole-star 

(often  called  Polaris)  being 
very  nearly  one  quarter  of 
the  distance  between  the  two 
"Pointers." 

14.  The  Celestial  Equator, 
or  Equinoctial ;  Declination.  — 
The  Equator  is  a  great  circle 
of  the  celestial  sphere  drawn 
half-way  between  the  poles, 
everywhere  90°  from  each  of 
them,  and  is  the  great  circle 
in  which  the  plane  of  the 
earth's  equator  cuts  the  celes- 
tial sphere.  It  is  often 
called  the  Equinoctial.  Fig.  5  shows  how  the  plane  of  the 
earth's  equator  produced  far  enough  would  mark  out  such 
a  circle  in  the  heavens. 

Small  circles  drawn  parallel  to  the  equinoctial,  like  the 
parallels  of  latitude  on  the  earth,  are  known  as  Parallels 
of  Declination,  the  Declination  of  a  star  being  its  distance 
in  degrees  north  or  south  of  the  celestial  equator  ;  +  if  north, 
-  if  south.     It  corresponds  precisely  with  the  latitude  of 
a  place  on  the  earth's  surface ;  but  it  cannot  be   called 
"  celestial  latitude,"  because  that  term  has  been  preoccupied 
by  an  entirely  different  quantity  (Sec.  20). 
i  See  Sec.  126. 


FIG.  5.— The  Plane  of  the  Earth's 
Equator  produced  to  cut  the  Celes- 
tial Sphere 


INTRODUCTION  15 

A  star's  parallel  of  declination  is  identical  with  its 
diurnal  circle. 

15.  Hour-Circles.  —  The   great  circles  of   the   celestial 
sphere  which  pass  through  the  poles  like  the  meridians  on 
the  earth,  and  are  therefore  perpendicular  to  the  celestial 
equator,  are  called  Hour-Circles.     Some  writers  call  them 
"  celestial  meridians,"  but  the  term  is  objectionable  since 
it  is  sometimes  used  to  indicate  an  entirely  different  set  of 
circles. 

That  particular  hour-circle  which  at  any  moment  passes 
through  the  zenith  of  course  coincides  with  the  celestial 
meridian  already  defined  in  Sec.  11. 

16.  The  Celestial  Meridian  and  the  Cardinal  Points.  - 
The  best  definition  of  the  celestial  meridian  is,  however, 
the  great  circle  which  passes  through  the  zenith  and  the  poles. 
The  points  where  this  meridian  cuts  the  horizon  (the  circle 
of  level)  are  the  north  and  south  points,  and  the  east  and 
west  points  of  the  horizon  lie  half-way  between  them,  the 
four  being  known  as  the  "  Cardinal  Points."     The  student 
is  especially  cautioned  against  confounding  the  north  poinl 
with  the  north  pole.     The  north  point  is  on4he  horizon; 
the  north  pole  is  high  up  in  the  sky. 

In  Fig.  6,  P  is  the  north  celestial  pole,  Z  is  the  zenith, 
and  SQZPN  is  the  celestial  meridian.  P  and  P'  are  the 
poles,  PmP'  is  the  hour-circle  of  m,  and  amRl  V  is  its  par- 
allel of  declination,  or  diurnal  circle.  N  and  S  are  the 
north  and  south  points  respectively.  In  the  figure,  mY  is 
the  declination  of  m,  and  mP  is  called  its  polar  distance. 

The  angle  made  at  the  celestial  pole  between  the  merid- 
ian and  the  hour-circle  passing  through  a  given  star  is 
called  the  star's  Hour-Angle  for  that  moment.  It  is 


16 


LESSONS  IN  ASTRONOMY 


usually  reckoned  westward  from  the  meridian,  and,  for  many 
purposes,  in  time  instead  of  in  arc,  i.e.,  in  hours,  minutes, 
and  seconds  of  time  instead  of  degrees,  etc.  One  hour 
=  15°,  and  one  minute  of  time  (lm)  =15  minutes  of  arc 
(15'),  etc.  The  hour-angle  of  a  star  is  always  equal  to  the 


FIG.  6.  —  Equator,  Hour-Circles,  etc. 


0,  place  of  the  observer  ;  Z,  his  zenith. 

S  WNE,  the  horizon. 

POP',  line  parallel  to  the  axis  of  the 
earth. 

P  and  P',  the  two  poles  of  the  heavens. 

EQWT,  the  celestial  equator,  or  equi- 
noctial. 

X,  the  vernal  equinox,  or  "first  of 
Aries." 

PXP',  the  equinoctial  colure,  or  zero 
hour-circle. 


TO,  some  star. 

Ym,  the  star's  declination;  Pm,  its 
north-polar  distance. 

Angle  mPH  =  a.TG  QY,  the  star's  (east- 
ern) hour-angle ;  =  24**  minus  star's 
western  hour-angle. 

Angle  XPm  =  arc  XY,  star's  right 
ascension. 

Sidereal  time  at  the  moment  =  2411  minus 
XPQ. 


interval  of  sidereal  time  (see  Sec.  91)  elapsed  since  the 
star  last  crossed  the  meridian. 

17,  The  Vernal  Equinox,  or  First  of  Aries.  —  In  order  to 
use  this  system  of  circles  as  a  means  of  designating  the 
places  of  stars  in  the  sky,  it  is  necessary  to  fix  upon  some 
one  hour-circle,  to  be  reckoned  from  in  the  same  way  that 


INTRODUCTION  17 

the  meridian  of  Greenwich  is  used  in  reckoning  longitude 
on  the  earth's  surface.  The  "  Greenwich  of  the  sky " 
which  has  thus  been  fixed  upon  is  the  point  where  the 
sun  crosses  the  celestial  equator  in  the  spring.  The  sun 
and  moon  and  the  planets  do  not  behave  as  if  they,  like 
the  stars,  were  firmly  fixed  upon  the  celestial  sphere,  but 
rather  as  if  they  were  glow-worms  crawling  slowly  about 
upon  its  surface  while  it  carries  them  in  its  diurnal  rota- 
tion. As  every  one  knows,  the  sun  in  winter  is  far  to 
the  south  of  the  equator,  and  in  the  summer  far  to 
the  north,  apparently  completing  a  yearly  circuit  of  the 
heavens  on  a  path  known  as  the  ecliptic.  It  crosses  the 
equator,  therefore,  twice  a  year,  passing  from  the  south 
side  of  it  to  the  north  about  March  21  (this  is  now 
true,  since  leap  year  was  skipped  in  1900),  and  always 
at  the  same  point)  neglecting  for  the  present  the  effect 
of  what  is  known  as  "precession."  This  point,  the 
celestial  Greenwich,  is  called  the  Vernal  Equinox,  and 
is  made  the  starting-point  for  many  astronomical  reckon- 
ings. Unfortunately  it  is  not  marked  by  any  conspicuous 
star;  but  a  line  drawn  from  the  Pole-star  through  Beta 
Cassiopeise  (the  westernmost  or  "  preceding "  star  in  the 
zigzag)  (see  Map  I)  and  continued  90°  from  the  pole, 
strikes  very  near  it.  In  Fig.  6,  X  represents  this  point. 
It  is  also  called  the  First  of  Aries,  and  designated  by  the 
symbol  °f> . 

18.  Right  Ascension.  —  The  right  ascension  of  a  star  is 
the  arc  of  the  celestial  equator  intercepted  between  the  vernal 
equinox  and  the  point  where  the  stars  hour-circle  cuts  the 
equator,  and  is  reckoned  always  eastward  from  the  equinox 
and  completely  around  the  circle.  It  may  be  expressed 


18  LESSONS  IN  ASTRONOMY 

either  in  degrees  or  in  hours.1  A  star  one  degree  west  of 
the  equinox  has  a  right  ascension  of  359°,  or  of  23h56m. 
Evidently  the  diurnal  motion  does  not  affect  the  right 
ascension  of  a  star,  but  this,  like  the  declination,  remains 
practically  unchanged  for  years.  In  Fig.  6,  if  X  be  the 
vernal  equinox,  the  right  ascension  of  m  is  the  arc  XY 
measured  from  X  eastward. 

19.  Thus  we  can  define  the  position  of  a  star  either  by 
its  altitude  and  azimuth,  which  tell  how  high  it  is  in  the 
sky,  and  how  it  "  bears,"  as  a  sailor  would  say ;  or  we 
may  use  its  right  ascension  and  declination,  which  do  not 
change  from  day  to  day  (not  perceptibly  at  least),  and  so 
are  better  adapted  to  mapping  purposes,  corresponding  as 
they  do  precisely  to  latitude  and  longitude  upon  the  surface 
of  the  earth. 

Perhaps  the  easiest  way  to  think  of  these  celestial  circles 
is  the  following:  Imagine  a  tall  pole  standing  straight  up 
from  the  observer,  having  attached  to  it  at  the  top  (the 
zenith)  two  half  circles  coming  down  to  the  level  of  the 
observer's  eye,  one  of  them  running  north  and  south 
(the  meridian),  and  the  other  east  and  west  (the  prime 
vertical).  The  bottoms  of  these  two  semicircles  are  con- 
nected by  a  complete  circle  (the  horizon)  at  the  level  of 
the  eye.  This  framework,  immense  but  fortunately  only 
imaginary  and  so  not  burdensome,  the  observer  takes 
with  him  wherever  he  goes,  keeping  always  at  its  center, 
while  over  it  apparently  turns  the  celestial  sphere ;  really, 
of  course,  he  and  the  earth  and  his  framework  turn 
together  under  the  celestial  sphere. 

1  Twenty-four  hours  of  right  ascension  or  hour-angle  =  360° ;  one 
hour  =  15°. 


INTRODUCTION  19 

The  other  circles  (the  celestial  equator  and  the  hour- 
circles)  are  drawn  upon  the  celestial  sphere  itself  and  are 
not  affected  at  all  by  the  observer's  journeys,  but  are  as 
fixed  as  the  poles  and  meridians  upon  the  earth;  the  stars 
also,  to  all  ordinary  observation,  are  fixed  upon  the  sphere 
just  as  cities  are  upon  the  earth.  They  really  move,  of 
course,  and  swiftly,  as  has  been  said  before,  but  they  are 
so  far  away  that  it  takes  centuries,  as  a  rule,  to  produce 
the  slightest  apparent  change  of  place. 

20.  Celestial  Latitude  and  Longitude.  —  A  different  way  of 
designating  the  positions  of  the  heavenly  bodies  in  the  sky  has  come 
down  to  us  from  very  ancient  times.  Instead  of  the  equator  it  makes 
use  of  another  circle  of  reference  in  the  sky,  known  as  the  Ecliptic. 
This  is  simply  the  apparent  path  described  by  the  sun  in  its  annual 
motion  among  the  stars;  for  the  sun  appears  to  creep  around  the 
celestial  sphere  in  a  circle  once  every  year,  and  the  Ecliptic  may  be 
defined  as  the  intersection  of  the  plane  of  the  earth's  orbit  with  the 
celestial  sphere,  just  as  the  celestial  equator  is  the  intersection  of  the 
earth's  equator ;  the  vernal  equinox  is  one  of  the  points  where  the  two 
circles  cross.  Before  the  days  of  clocks,  the  Ecliptic  was  in  many 
respects  a  more  convenient  circle  of  reference  than  the  equator  and 
was  almost  universally  used  as  such  by  the  old  astronomers.  Celestial 
longitude  and  latitude  are  measured  with  reference  to  the  Ecliptic, 
in  the  same  way  that  right  ascension  and  declination  are  measured 
with  respect  to  the  equator,  except  that  celestial  longitude  cannot  be 
expressed  in  hours,  minutes,  and  seconds  of  time  like  right  ascen- 
sion. Too  much  care  can  hardly  be  taken  to  avoid  confusion  between 
terrestrial  latitude  and  longitude  and  the  celestial  quantities  that  bear 
the  same  name. 


CHAPTER  II 


URANOGRAPHY 

Globes  and  Star-Maps  —  Star  Magnitudes  —  Designation  of  the  Stars  —  The 
Constellations 

NOTE.  —  It  is  hardly  necessary  to  say  that  this  chapter  is  to  be 
treated  by  the  teacher  differently  from  the  rest  of  the  book.  It  is  to 
be  dealt  with,  not  as  recitation  matter,  but  as  field-work :  to  be 
taken  up  at  different  times  during  the  course  as  the  constellations 
make  their  appearance  in  the  evening  sky. 

For  convenience  of  reference  we  add  the  following  alphabetical 
list  of  the  constellations  described  or  mentioned  in  the  chapter : 


ARTICLE 

AndrdmSda 35 

Anser,  see  Vulpe"cula  ...  69 

Antinoiis,  see  Aqulla  .     .     .  71 

Antlia 62 

Aquarius 78 

Aqulla  (not  Aquila)  .      .     .  71 

Argo  Navis 51 

Aries 38 

Auriga 41 

Bootes 59 

Camelopdrdalis 31 

Cancer 52 

Canes  Venatici       ....  58 

Canis  Major 49 

Canis  Minor 48 

Capricornus 73 

Cassi6p<§ia 28 


ARTICLE 

Centaurus 62 

Cepheus 29 

Cetus 39 

Columba 45 

Coma  Ber8nices     ....  57 

Corona  Borealis      .     .     .  (  .  60 

Corvus 55 

Crater 55 

Cygnus 68 

Delphmus 74 

Draco 30 

Equiileus 75 

Erldanus 44 

Gemini 47 

Grus 79 

Hercules 66 

Hydra 55 


20 


URANOGRAPHY 


21 


ARTICLE 

Lacerta 76 

Leo 53 

Leo  Minor 54 

Lepus .45 

Libra  .     ..  ..   U    ,     ...  61 

Lupus       .    -i    v    .     .     .     ,  62 

Lynx   .     ,-   i   v  ';•.'.     .     .  46 

Lyra    .     ...    „     .    -.     .     .  67 

Monoceros 50 

Norma      .  "  .     '."   ....  64 

Ophiuchus    .     .     .•  '.     .     .  65 

Orion  .     .     .     .:  i.  .;     .     .  43 

Pegasus    .  ...iVy,  !,»;.  -.     .     .  77 

Perseus     .          40 

Phoenix    .."../.     .     .     .  39 

Pisces  .  36 


ARTICLE 

Piscis  Australis      .'..-.  79 

(Pleiades)     ......  42 

Sagitta 70 

Sagittarius 72 

Scorpio 63 

Sculptor  .     .     .     .     .     .     .39 

Serpens 65 

Serpentarius,  see  Ophiuchus  65 

Sextans    .     .     .  , .     .     .     .  54 

Taurus 42 

Taurus  Poniatovii       ...  65 

Triangulum  ......  37 

Ursa  Major 2& 

Ursa  Minor  ......  27 

Virgo. 56 

VulpSctila 69 


21.  Globes  and  Star-Maps.  —  In  order  to  study  the  con- 
stellations conveniently,  it  is  necessary  to  have  either  a 
celestial  globe  or  a  star-map,  by  which  to  identify  the 
stars.     The  globe  is  better  and  more  accurate,  if  of  suffi- 
cient size,  but  is  costly  and  rather  inconvenient.     (For  a 
figure  and  description  of  the  globe,  see  Appendix,  Sec.  400.) 
For  most  purposes  a  star-map  will  answer  just  as  well  as 
the  globe,  but  it  can  never  represent  any  considerable  por- 
tion of  the  sky  correctly  without  more  or  less  distortion  of 
all  the  lines  and  figures  near  the  margin  of  the  map.     Such 
maps  are  made  on  various  systems,  each  presenting  its  own 
advantages.     In  all  of  them  the  heavens  are  represented 
as  seen  from  the  inside,  and  not  as  on  the  globe,  which 
represents  the  sky  as  if  seen  from  the  outside. 

22,  Star-Maps  of  this  Book.  —  We  present  a  series  of 
four  small  maps,  which,  though  hardly  on  a  large  enough 


22  LESSONS  IN  ASTRONOMY 

scale  to  answer  every  purpose  of  a  complete  celestial  atlas, 
are  quite  sufficient  to  enable  the  student  to  trace  out  the 
constellations,  and  to  identify  the  principal  stars.  In  the 
map  of  the  north  circumpolar  regions  (Map  I)  the  pole  is 
in  the  center,  and  at  the  circumference  are  numbered  the 
twenty-four  hours  of  right  ascension.  The  parallels  of  dec- 
lination are  represented  by  equidistant  concentric  circles. 
On  the  three  other  rectangular  maps,  which  show  the  equa- 
torial belt  of  the  heavens  lying  between  50°  north  and 
50°  south  of  the  equator,  the  parallels  of  declination  are 
horizontal  lines,  while  the  hour-circles  are  represented  by 
vertical  lines,  also  equidistant,  but  spaced  at  a  distance 
which  is  correct,  not  at  the  equator  but  for  declination  35°. 
This  keeps  the  distortion  within  reasonable  bounds,  even 
near  the  margin  of  the  map,  and  makes  it  very  easy  to  lay 
off  the  places  of  any  object  for  which  the  right  ascension 
and  declination  are  given.  The  ecliptic  is  the  curved  line 
which  extends  across  the  middle  of  the  map.  The  top  of 
the  map  is  north;  and  the  east  is  to  the  left,  instead  of 
being  at  the  right  hand,  as  in  a  map  of  the  earth's  sur- 
face ;  so  that  if  the  observer  faces  the  south,  and  holds  the 
map  up  before  and  above  him,  the  constellations  which  are 
near  the  meridian  will  be  pretty  truly  represented. 

The  hours  of  right  ascension  are  indicated  on  the  central  hori- 
zontal line,  which  is  the  celestial  equator,  and  at  the  top  of  the  map 
are  given  the  names  of  the  months.  The  word  "  September,"  for 
instance,  means  that  the  stars  which  are  directly  under  it  on  the  map 
will  be  near  the  meridian  about  9  o'clock  in  the  evening  during  that 
month. 

23.  Star  Magnitudes.  —  To  the  eye  the  principal  differ- 
ence in  the  appearance  of  the  different  stars  is  in  their 


URANOGRAPHY  23 

brightness,  or  their  so-called  "  magnitude."  Hipparchus 
(125  B.C.)  and  Ptolemy  divided  the  visible  stars  into  six 
classes,  the  brightest  fifteen  or  twenty  being  called  first- 
magnitude  stars,  and  the  faintest  which  can  be  seen  by 
the  naked  eye  being  called  sixth. 

It  has  since  been  found  that  the  light  of  the  average  first-magni- 
tude star  is  just  about  one  hundred  times  as  great  as  that  of  the 
sixth ;  and  at  this  rate  the  light  of  a  first-magnitude  star  should  be 
a  trifle  more  than  equal  to  two  and  a  half  second-magnitude  stars, 
and  a  second-magnitude  star,  to  two  and  a  half  third-magnitude 
stars,  etc. 

Our  maps  show  all  the  stars  down  to  the  fifth  magnitude 
—  about  a  thousand  in  number  —  and  all  which  can  be 
seen  in  a  moonlight  night.  A  few  smaller  stars  are  also 
inserted  where  they  mark  some  particular  configuration 
or  point  out  some  interesting  telescopic  object.  A  varia- 
ble star  is  denoted  by  var.  below  the  star  symbol.  A  few 
clusters  and  nebulae  are  also  indicated.  The  letter  M. 
against  one  of  these  stands  for  "  Messier,"  who  made  the 
first  catalogue  of  103  such  objects  in  1784;  e.g.,  M.  51 
designates  No.  51  on  Messier's  list. 

For  reference  purposes  and  for  study  of  the  heavens  in  detail,  the 
more  elaborate  star-atlases  of  Proctor,  Heis,  Upton,  or  Schurig  are 
recommended,  especially  the  last,  which  contains  a  great  amount 
of  useful  information  in  addition  to  the  maps,  and  is  very  cheap 
compared  with  the  others.  The  student  or  teacher  who  possesses  a 
telescope  will  also  find  an  invaluable  accessory  to  it  in  Webb's 
"  Celestial  Objects  for  Common  Telescopes."  (Published  by  Long- 
mans, Green  fy  Co.,  New  For/:.) 

24,  Designation  of  the  Stars.  —  A  few  of  the  brighter 
stars  are  designated  by  names  of  their  own,  and  upon  the 


24  LESSONS  IN  ASTRONOMY 

map  those  names  which  are  in  most  common  use  are  indi- 
cated.1 Generally,  however,  the  designation  of  visible  stars 
is  by  the  letters  of  the  Greek  alphabet,  on  a  plan  proposed 
in  1603  by  Bayer,  and  ever  since  followed.  The  letters 
are  ordinarily  applied  nearly  in  the  order  of  brightness, 
Alpha  being  the  brightest  star  in  the  constellation  and 
Beta  the  next  brightest;  but  they  are  sometimes  applied 
to  the  stars  in  their  order  of  position  rather  than  in  that 
of  brightness.  When  the  stars  of  a  constellation  are  so 
numerous  as  to  exhaust  the  letters  of  the  Greek  alphabet, 
the  Roman  letters  are  next  used,  —  and  then,  if  necessary, 
we  employ  the  numbers  which  Flamsteed  assigned  a  cen- 
tury later.  At  present  every  star  visible  to  the  naked  eye 
can  be  referred  to  and  identified  byv  its  number  or  letter  in 
the  constellation  to  which  it  belongs.  (For  the  Greek 
alphabet,  see  Appendix,  page  406.) 

25.  We  begin  our  study  of  Uranography  with  the  con- 
stellations which  are  circumpolar  (Le.,  within  40°  of  the 
north  pole),  because  these  are  always  visible  in  the  tJnited 
States  and  so  can  be  depended  on  to  furnish  land-  (or 
rather  sky]  marks  to  aid  in  tracing  out  the  others.  Since 
in  the  latitude  of  New  York  the  elevation  of  the  pole  is 
about  41°,  it  follows  that  there  (and  this  is  approximately 
true  of  the  rest  of  the  United  States)  all  the  constella- 
tions which  are  within  41°  of  the  north  pole  will  move 
around  it  once  in  twenty-four  hours  without  setting.  For 
this  reason  they  are  called  circumpolar.  Map  I  contains 
them  all. 

aBy  far  the  best  book  upon  the  subject  of  stellar  nomenclature  is 
Allen's  ' '  Star-Names  and  their  Meanings. "  It  is  full  of  interesting  matter 
relating  to  the  constellations  and  the  myths  and  legends  attached  to  them. 


URANOGRAPHY  25 

26.  Ursa  Major,  the  Great  Bear  (Map  I).  —  Of  these 
circumpolar  constellations  none  is  more  easily  recognized 
than  Ursa  Major.  Assuming  the  time  of  observation  as 
about  8  o'clock  in  the  evening  on  September  22,  it  will  be 
found  below  the  pole  and  to  the  west.  Hold  the  map  so 
that  VIII  is  at  the  bottom,  and  it  will  be  rightly  placed 
for  the  time  assumed. 

The  familiar  Dipper  is  sloping  downward  in  the  north- 
west, composed  of  seven  stars,  all  of  about  the  second  mag- 
nitude, excepting  Delta  (at  the  junction  of  the  handle  to  the 
bowl),  which  is  of  the  third  magnitude.  The  stars  Alpha 
(Dubhe)  and  Beta  (Merak)  are  known  as  the  "Pointers," 
because  a  line  drawn  from  Beta  through  Alpha  and  pro- 
duced about  30°  passes  very  near  the  Pole-star.  The 
dimensions  of  the  Dipper  furnish  a  convenient  scale  of 
angular  measure.  From  Alpha  to  Beta  is  5°;  from  Alpha 
to  Delta  is  10° ;  and  from  Alpha  to  Eta,  at  the  extremity 
of  the  Dipper-handle  (which  is  also  the  Bear's  tail),  is  26°. 
The  Dipper  (known  also  in  England  as  the  "  Plough  "  and 
as  the  "  Wain,"  or  wagon)  comprises  but  a  small  part  of 
the  whole  constellation.  The  head  of  the  Bear,  indicated 
by  a  small  group  of  scattered  stars,  is  nearly  on  the  line 
from  Delta  through  Alpha,  carried  on  about  15° ;  at  the 
time  assumed  (September  22,  8  o'clock)  it  is  almost  exactly 
under  the  pole. 

Three  of  the  four  paws  of  the  creature  are  marked  each 
by  a  pair  of  third-  or  fourth-magnitude  stars  li°  or  2° 
apart.  The  three  pairs  are  nearly  equidistant,  about  20° 
apart,  and  almost  on  a  straight  line  parallel  to  the  diagonal 
of  the  Dipper-bowl  from  Alpha  to  Gamma,  but  some  20° 
south  of  it.  At  the  time  assumed  they  are  all  three  very 


26  LESSONS  IN  ASTRONOMY 

near  the  horizon  for  an  observer  in  latitude  40°,  but  during 
the  spring  or  summer,  when  the  constellation  is  high  in 
the  sky,  they  can  be  easily  made  out. 

The  star  Zeta  (Mizar),  at  the  bend  in  the  handle,  is 
easily  recognized  by  the  little  star  Alcor  near  it.  Mizar 
itself  is  a  double  star,  easily  seen  as  double  with  a  small 
telescope,  and  one  of  the  most  interesting  recent  astro- 
nomical results  is  the  discovery  that  it  is  really  triple,  the 
larger  of  the  two  stars  being  itself  a  "  spectroscopic  double," 
invisibly  so  to  the  telescope,  but  revealing  its  double  char- 
acter by  means  of  the  lines  in  its  spectrum.  (See  Sec.  373.) 
The  star  Xi,  the  southern  one  of  the  pair,  which  marks  the 
left-hand  paw,  is  also  double  and  binary,  i.e.,  the  two  stars 
which  compose  it  revolve  about  their  common  center  of 
gravity  in  .about  sixty-one  years.  (For  diagram  of  the 
orbit,  see  Fig.  89,  Sec.  369.)  It  was  the  first  binary  whose 
orbit  was  computed. 

According  to  the  ancient  legends,  Ursa  Major  is  Callisto,  the 
daughter  of  Lycaon,  king  of  Arcadia.  The  jealousy  of  Juno1 
-changed  her  into  a  bear,  and  afterwards  Jupiter  placed  her  among 
the  constellations  with  Areas  her  son,  who  became  Ursa  Minor. 
One  of  the  quaint  old  authors  explains  the  very  un-bearlike  length 
of  the  creatures'  tails  by  saying  that  they  stretched  as  Jupiter  lifted 
them  to  the  sky. 

27.  Ursa  Minor,  the  Lesser  Bear  (Map  I).  —  The  line 
of  the  Pointers  unmistakably  marks  out  the  Pole-star 

1  We  have  followed  throughout  the  Eoman  nomenclature  of  the  gods 
•  and  heroes,  as  used  by  Virgil  and  Ovid;  but  the  reader  should  be  reminded 
that,  in  many  important  respects,  these  Koman  personages  differ  from 
the  Greek  divinities  who  were  identified  with  them.  It  should  be  said, 
also,  that  in  many  cases  the  old  legends  are  greatly  confused  and  often 
contradictory ;  as,  for  instance,  in  the  case  of  Hercules. 


URANOGRAPHY  27 

(Polaris],  a  star  of  the  second  magnitude,  standing  quite 
alone.  It  is  at  the  end  of  the  tail  of  Ursa  Minor,  or  at 
the  extremity  of  the  handle  of  the  "Little  Dipper";  for 
in  Ursa  Minor,  also,  the  seven  principal  stars  form  a  dipper, 
though  with  the  handle  bent  in  a  different  way  from  that 
of  the  other  Dipper.  Beginning  at  Polaris,  a  curved  line 
(concave  towards  Ursa  Major)  drawn  through  Delta  and 
Epsilon  brings  us  to  Zeta,  where  the  handle  joins  the 
bowl.  Two  bright  stars  (second  and  third  magnitude), 
Beta  and  Gamma,  correspond  to  the  Pointers  in  the  large 
Dipper,  and  are  known  as  the  "Guardians  of  the  Pole"; 
Beta  is  named  Kochab.  The  pole  now  lies  about  li°  from 
the  Pole-star,  on  the  line  joining  it  to  Mizar  (at  the  bend 
in  the  handle  of  the  large  Dipper). 

It  has  not  always  been  so.  Some  4000  years  ago  the  star  Thuban 
(Alpha  Draconis)  was  the  Pole-star,  and  2000  years  ago  the  present 
Pole-star  was  very  much  farther  from  the  pole  than  now.  At  present 
the  pole  is  coming  nearer  to  the  star,  and  towards  the  close  of  the  next 
century  it  will  be  within  half  a  degree  of  it.  Twelve  thousand  years 
hence  the  bright  star  Alpha  Lyrse  will  be  the  Pole-star,  —  and  this  not 
because  the  stars  change  their  positions,  but  because  the  axis  of  the 
earth  slowly  changes  its  direction,  owing  to  precession.  (See  Sec.  125.) 

The  Greek  name  of  the  Pole-star  was  Cynosura,  which 
means  the  "  tail  of  the  Dog,"  indicating  that  at  one  time 
the  constellation  was  understood  to  represent  a  Dog  instead 
of  a  Bear. 

As  already  said  (Sec.  26),  this  constellation  is  by  many  writers 
identified  with  Areas,  Callisto's  son.  But  more  generally  Areas  is 
identified  with  Bootes. 

The  Pole-star  is  double,  having  a  small  companion  barely 
visible  with  a  telescope  of  two  or  three  inches  diameter. 


28  LESSONS  IN  ASTRONOMY 

28,  Cassiopeia  (Map  I).  —  This  constellation  lies  on  the 
opposite  side  of  the  pole  from  the  Dipper,  and  at  about 
the  same  distance  from  it  as  the  Pointers.  It  is  easily 
recognized  by  the  zigzag,  "rail-fence  "configuration  of  the 
five  or  six  bright  stars  that  mark  it.  With  the  help  of 
the  rather  inconspicuous  star  Kappa,  one  can  make  out  of 
them  a  pretty  good  chair  with  the  feet  turned  away  from 
the  pole.  But  this  is  wrong.  In  the  recognized  figures 
of  the  constellation  the  lady  sits  with  feet  towards  the 
pole,  and  the  bright  star  Alpha  is  in  her  bosom,  while 
Zeta  and  the  other  faint  stars  south  of  Alpha  are  in  her 
head  and  uplifted  arms ;  Iota,  on  the  line  from  Delta  to 
Epsilon  produced,  is  in  the  foot.  The  order  of  the  prin- 
cipal stars  is  easily  remembered  by  the  word  "  Bagdei," 
i.e..  Beta,  Alpha,  Gamma,  Delta,  Epsilon,  Iota. 

Alpha,  which  is  slightly  variable  in  brightness,  is  known 
as  Schedir;  Beta  is  called  Caph.  The  little  star  Eta,  which 
is  about  half-way  between  Alpha  and  Gamma,  a  little  off  the 
line,  is  a  very  pretty  double  star,  —  the  larger  star  orange, 
the  smaller  one  purple.  It  is  binary  (i.e.,  the  two  stars  re- 
volve around  each  other),  with  a  period  of  about  206  years. 

In  the  year  1572  a  famous  temporary  star  made  its 
appearance  in  this  constellation,  at  a  point  on  the  line 
drawn  from  Gamma  through  Kappa,  and  extended  about 
half  its  length.  It  was  carefully  observed  and  described 
by  Tycho  Brahe,  and  at  one  time  was  bright  enough  to  be 
seen  easily  in  broad  daylight.  There  has  been  an  entirely 
unfounded  notion  that  this  was  identical  with  the  star  of 
Bethlehem,  and  there  has  been  an  equally  unfounded 
impression  that  its  reappearance  may  be  expected  about 
the  present  time. 


URANOGRAPHY  29 

Cassiopeia  was  the  wife  of  Cepheus,  king  of  Libya,  and  the  mother 
of  Andromeda,  who  was  rescued  from  the  sea-monster,  Cetus,  by  Per- 
seus, who  came  flying  through  the  air,  and  used  the  head  of  Medusa 
(which  he  still  holds  in  his  hand)  to  turn  his  adversaries  to  stone. 
Cassiopeia  had  indulged  in  too  great  boasting  of  her  daughter's 
beauty,  and  thus  excited  the  jealousy  of  the  Nereids,  at  whose  insti- 
gation the  sea-monster  was  sent  by  Neptune  to  ravage  the  kingdom. 

29.  Cepheus  (Map  I).  —  This  constellation,  though  large, 
contains  very  few  bright  stars.     At  the  assumed  time  (8 
o'clock,  September  22)  it  is  above  Cassiopeia  and  to  the 
west,  not  having  quite  reached  the  meridian  above  the 
pole.    A  line  carried  from  Alpha  Cassiopeia  through  Beta, 
and  produced  20°,  will  pass  very  near  to  Alpha  Cephei,  a 
star  of  the  third  magnitude  in  the  king's  right  shoulder. 
Beta  Cephei  is  about  8°  north  of  Alpha,  and  Gamma  about 
12°  from  Beta,  both  also  of  the  third  magnitude.     Gamma 
is  so  placed  that  it  is  at  the  obtuse  angle  of  a  rather  flat 
isosceles  triangle  of  which  Beta  Cephei  and  the  Pole-star 
form  the  other  two  corners.     Cepheus  is  represented  as 
sitting  behind  Cassiopeia  (his  wife)  with   his  feet  upon 
the  tail  of  the  Little  Bear,  Gamma  being  in  his  left  knee. 
His  head  is  marked  by  a  little  triangle  of  fourth- magnitude 
stars,  of  which  Delta  is  a  remarkable  variable  with  a  period 
of  5|  days.    It  is  worth  noting  that  there  are  several  other 
small  variable  stars  in  the  same  neighborhood  (none  of  them 
bright  enough  to  be  shown  upon  the  map).    Beta  is  a  very 
pretty  double  star. 

30.  Draco,  the  Dragon  (Map  I).  —  The  constellation  of 
Draco  is  characterized  by  a  long,  winding  line  of  stars, 
mostly  small,  extending   half-way  around   the    pole   and 
separating  the  two  Bears.     A  line  from  Delta  Cassiopeia 
drawn  through  Beta  Cephei  and  extended  about  as  far 


30  LESSONS  IN  ASTRONOMY 

again  will  fall  upon  the  head  of  Draco,  marked  by  an 
irregular  quadrilateral  of  stars,  two  of  which  are  of  the  2£ 
and  3  magnitude.  These  two  bright  stars  about  4°  apart 
are  Beta  and  Gamma.  The  latter  (named  Etaniri),  in  its 
daily  revolution,  passes  almost  exactly  through  the  zenith 
of  Greenwich,  and  it  was  by  observations  upon  it  that  the 
"aberration  of  light"  was  discovered.  (See  Sec.  435.) 
The  nose  of  Draco  is  marked  by  a  smaller  star,  Mu,  some 
6°  beyond  Beta,  nearly  on  the  line  drawn  through  it  from 
Gamma.  From  Gamma  we  trace  the  neck  of  Draco,  east- 
ward and  downward1  toward  the  Pole-star,  until  we  come 
to  Delta  and  Epsilon  and  some  smaller  stars  near  them. 

There  the  direction  of  the  line  is  reversed,  as  shown 
upon  the  map,  so  that  the  body  of  the  monster  lies  between 
its  own  head  and  the  bowl  of  the  Little  Dipper,  and  winds 
around  this  bowl  until  the  tip  of  the  tail  is  reached,  at  the 
middle  of  the  line  between  the  Pointers  and  the  Pole-star. 
The  constellation  covers  more  than  twelve  hours  of  right 
ascension. 

One  star  deserves  special  notice,  the  star  Alpha,  or 
Thuban,  a  star  of  3£  magnitude,  which  lies  half-way 
between  Zeta  Ursae  Majoris  (Mizar)  and  Gamma  Ursa 
Minoris.  Four  thousand  seven  hundred  years  ago  it  was 
the  Pole-star,  and  then  within  a  quarter  of  a  degree  of 
the  pole,  much  nearer  than  Polaris  is  at  present  or  ever 
will  be.  It  is  probable  also  that  its  brightness  has  con- 
siderably fallen  off  within  the  last  200  years,  since  among 
the  ancient  astronomers  it  was  always  reckoned  as  of  the 
second  magnitude  and  is  not  now  much  above  the  fourth. 

1  The  description  applies  strictly  only  at  the  time  assumed,  8  o'clock, 
September  22. 


URANOGRAPHY  31 

The  so-called  "  Pole  of  the  Ecliptic  "  is  in  this  constella- 
tion, i.e.,  the  point  which  is  90°  distant  from  every  point 
in  the  Ecliptic,  the  circle  annually  described  by  the  sun. 
This  point  (see  map)  is  the  center  around  which  precession 
causes  the  pole  to  move  nearly  in  a  circle  (see  Sec.  126) 
once  in  25,800  years. 

The  mythology  of  this  constellation  is  doubtful.  According  to 
some  it  is  the  dragon  which  Cadmus  slew,  afterwards  sowing  its  teeth, 
from  which  sprung  up  the  harvest  of  armed  men  who  fought  and  slew 
each  other,  leaving  only  the  five  survivors  who  were  the  founders  of 
Thebes.  Others  say  that  it  was  the  dragon  who  watched  the  golden 
apples  of  the  Hesperides,  and  was  killed  by  Hercules  when  he  cap- 
tured that  prize.  This  accords  best  with  the  fact  that  in  the  heavens 
Hercules  has  his  foot  on  the  dragon's  head. 

31.  Camelopardalis. — This  is  the  only  remaining  one  of  the  strictly 
circumpolar  constellations,  —  a  modern  one  containing  no  stars  above 
fourth  magnitude,  and  established  by  Hevelius  (1611-1687)  simply  to 
cover  the  great  empty  space  between  Cassiopeia  and  Perseus  on  one 
side,  and  Ursa  Major  and  Draco  on  the  other.     The  animal  stands 
on  the  head  and  shoulders  of  Auriga,  and  his  head  is  between  the 
Pole-star  and  the  tip  of  the  tail  of  Draco. 

The  two  constellations  of  Perseus  (which  at  the  time  assumed  is 
some  20°  below  Cassiopeia)  and  of  Auriga  are  partly  circumpolar, 
but  on  the  whole  can  be  more  conveniently  treated  in  connection 
with  the  equatorial  maps.  Capella,  the  brightest  star  of  Auriga, 
and  next  to  Vega  and  Arcturus  the  brightest  star  in  the  northern 
hemisphere,  is  at  the  time  assumed  (8  o'clock,  September  22)  a  few 
degrees  above  the  horizon  in  the  northeast.  Between  it  and  the  nose 
of  Ursa  Major  lies  part  of  the  constellation  of  the  Lynx,  a  modern 
one,  made,  like  Camelopardalis,  by  Hevelius  merely  to  fill  a  gap,  and 
without  any  large  stars. 

32.  The  Milky  Way  in  the  Circumpolar  Region The 

only  circumpolar  constellations    traversed  by  the  Milky 
Way  are  Cassiopeia  and  Cepheus.   It  enters  the  circumpolar 


32  LESSONS  IN  ASTRONOMY 

region  from  the  constellation  of  Cygnus,  which  at  the 
assumed  time  is  near  the  zenith,  sweeps  down  across 
the  head  and  shoulders  of  Cepheus,  and  on  through 
Cassiopeia  and  Perseus  to  the  northeastern  horizon  in 
Auriga.  There  is  one  very  bright  patch  a  few  degrees 
north  of  Beta  Cassiopeia,  and  half-way  between  Delta 
Cassiopeise  and  Gamma  Persei  there  is  another  bright 
cloud  in  which  is  the  famous  double  cluster  of  the 
"  sword-handle  of  Perseus,"  —  a  beautiful  object  for  even 
the  smallest  telescope. 

33.  For  the  most  part  the  constellations  shown  upon 
the  circumpolar  map  (I)  will  be  visible  every  night  in  the 
northern  part  of  the  United   States.     At  places  farther 
south  the   constellations  near  the   rim  of  the  map  will 
stay  below  the  horizon  for  a  short  time  every  twenty- 
four  hours,  since  the  height  of  the  pole  always  equals  the 
latitude  of   the   observer,  and  therefore  only  those  stars 
which  have  a  polar  distance   less  than  the  latitude  will 
remain  constantly  visible.     In  other  words,  if,  with  the 
pole  as  a  center,  we  draw  a  circle  with  a  radius  equal  to 
the  height  of  the  pole  above  the  horizon,  all  the   stars 
within    this    circle    will    remain    continually   above    the 
horizon.     This  is  called  the  circle  of  "  Perpetual  Appa- 
rition" (Sec.  85).     At  New  Orleans,  in  latitude  30°,  its 
radius,  therefore,  is  only  30°,  and  only  those  stars  which 
are  within  30°  of  the  pole  will  make  a  complete  circle 
without  setting.     At  stations  in  the  northern  part  of  the 
United  States,  as  Tacoma,   it  is  nearly  as  large   as  the 
whole  map. 

34.  Before  proceeding  to  consider  the  other  constella- 
tions, the  student  should  be  reminded  that  he  will  have 


URANOGRAPHY  33 

to  select  those  that  are  conveniently  visible  at  the  time 
of  the  year  when  he  happens  to  be  studying  the  subject, 
and  that,  if  he  wishes  to  cover  the  whole  sky,  he  must  take 
up  the  subject  more  than  once,  and  at  various  seasons  of  the 
year.  The  constellations  near  the  southern  limits  of  the 
map  can  be  seen  only  a  few  weeks  in  each  year. 

He  will  also  be  likely  to  be  occasionally  perplexed  by 
finding  in  the  heavens  certain  conspicuous  stars  not  on 
the  maps,  —  stars  much  brighter  than  any  that  are  given. 
These  are  the  planets  Venus,  Jupiter,  Mars,  and  Saturn, 
called  planets — i.e.,  "  wandering  stars  "  —just  because  they 
continually  change  their  place,  and  so  cannot  be  mapped. 
The  student  will  find  it  interesting  and  instructive,  how- 
ever, to  dot  down  upon  the  star-map  every  clear  night  the 
places  of  any  planets  he  may  notice,  and  thus  to  follow 
their  motion  for  a  month  or  two. 

Remember  also  that  on  these  maps  east  always  lies  on 
the  left  hand,  so  that  the  map  should  be  held  between 
the  eye  and  the  sky  in  order  to  represent  things  cor- 
rectly. We  begin  with  Andromeda  at  the  northwest 
corner  of  Map  II. 

35.  Andromeda  (Maps  II  and  IV) .  November. — Andromeda 
will  be  found  exactly  overhead  in  our  latitudes  about 
"9  o'clock  in  the  middle  of  November.  Its  characteristic 
configuration  is  the  line  of  three  second-magnitude  stars, 
Alpha,  Beta,  and  Gamma,  extending  east  and  north  from 
Alpha  (Alpheratz),  which  itself  forms  the  northeast  corner 
of  the  so-called  "  Great  Square  of  Pegasus,"  and  is  some- 
times lettered  as  Delta  Pegasi.  This  star  may  readily  be 
found  by  extending  an  imaginary  line  from  Polaris  through 
Beta  Cassiopeise  and  producing  it  about  as  far  again ;  Alpha 


34  LESSONS  IN  ASTRONOM1 

is  in  the  head  of  Andromeda,  Beta  (Mirach)  in  her  waist, 
and  Gamma  (Almaach)  in  her  left  foot.  A  line  drawn 
northwesterly  from  Beta,  nearly  at  right  angles  to  the 
line  Beta  Gamma,  will  pass  through  Mu  at  a  distance  of 
about  5°,  and  produced  another  5°  will  strike  the  "  great 
nebula,"  which  is  visible  to  the  naked  eye  like  a  little 
cloud  of  light,  and  forms  a  small  obtuse-angled  triangle 
with  Nu  and  a  little  sixth-magnitude  star.  Andromeda 
has  her  mother,  Cassiopeia,  close  by  on  the  north,  with 
her  father,  Cepheus,  not  far  away,  while  at  her  feet  is 
Perseus,  her  deliverer.  Her  head  rests  upon  the  shoulder 
of  Pegasus.  In  the  south,  beyond  the  constellations  of 
Aries  and  Pisces,  Cetus,  the  sea-monster,  who  was  to  have 
devoured  her,  stretches  his  ungainly  bulk. 

We  have 'already  mentioned  the  nebula.  Another  very  pretty 
object  is  Gamma,  which  in  a  small  instrument  is  a  double  star,  the 
larger  one  orange,  the  smaller  a  greenish  blue.  The  small  star  is 
itself  double,  making  the  system  really  triple,  but  as  such  is  beyond 
the  reach  of  any  but  very  large  instruments. 

When  Neptune  sent  the  leviathan,  Cetus,  to  ravage  Libya,  the 
oracle  of  Ammon  announced  that  the  kingdom  could  be  delivered 
only  if  Cepheue  would  give  up  his  daughter.  He  assented  and 
chained  the  poor  girl  to  a  rock  to  await  her  destruction.  But  Per- 
seus, returning  through  the  air  from  the  slaying  of  the  Gorgon, 
Medusa,  saw  her,  rescued  her,  won  her  love,  and  made  her  his  wife. 

36,  Pisces,  the  Fishes  (Map  II).  November.  —  Imme- 
diately south  of  Andromeda  lies  Pisces,  the  first  of  the  con- 
stellations of  the  Zodiac,1  which  is  a'belt  16°  wide  (8°  on 

1  The  word  is  derived  from  the  Greek  word  zoon  (  a  living  creature) 
and  indicates  that  all  the  constellations  in  it  (Libra  alone  excepted)  are 
animals.  The  zodiacal  constellations  are  for  the  most  part  of  remote 
antiquity,  antedating  by  many  centuries  even  the  Greek  mythology. 


URANOGRAPHY  35 

each  side  of  the  ecliptic),  encircling  the  heavens,  and 
including  the  space  within  the  limits  of  which  the  sun,  the 
moon,  and  all  the  principal  planets  perform  their  apparent 
motions.  At  present,  in  consequence  of  precession,  it 
occupies  the  sign  of  Aries.  (See  Sec.  126.)  It  has  not  a 
single  conspicuous  star,  and  is  notable  only  as  now  con- 
taining the  Vernal  Equinox,  or  First  of  Aries,  which  lies 
near  the  southern  boundary  of  the  constellation  in  a  pecul- 
iarly starless  region.  A  line  from  Alpha  Andromedae 
through  Gamma  Pegasi,  continued  as  far  again,  strikes 
about  2°  east  of  the  point.  The  body  of  one  of  the  two 
fishes  lies  about  15°  south  of  the  middle  of  the  southern 
side  of  the  "  Great  Square  of  Pegasus,"  and  is  marked  by 
an  irregular  polygon  of  small  stars,  5°  or  6°  in  diameter. 
A  long  crooked  "  ribbon "  of  little  stars  runs  eastward 
for  more  than  30°,  terminating  in  Alpha  Piscium  (called 
El  Rischa,  or  "  the  knot "),  a  star  of  the  fourth  magni- 
tude 20°  south  of  the  head  of  Aries.  From  there  another 
line  of  stars  leads  up  northwest  in  the  direction  of  Delta 
Andromedse  to  the  northern  fish,  which  lies  in  the  vacant 
space  south  of  Beta  Andromedse. 

Alpha  is  a  very  pretty  double  star,  the  two  components  being 
about  2"  apart. 

The  mythology  of  this  constellation  is  not  very  well  settled.  One 
story  is  that  the  fishes  are  Venus  and  her  son  Cupid,  who  were  thus 
transformed  when  endeavoring  to  escape  from  the  giant  Typhon. 
The  northern  fish  is  Cupid,  the  southern  his  mother. 

37.  Triangulum,  or  Deltoton,  the  Triangle  (Map  II). 
December.  —  This  little  constellation,  insignificant  as  it 
is,  is  one  of  Ptolemy's  ancient  forty-eight.  It  lies  half-way 
between  Gamma  Andromeda  and  the  head  of  Aries,  and 


36  LESSONS  IN  ASTRONOMY 

is  characterized  by  three  stars  of  the  third  and  fourth  mag- 
nitude, easily  made  out  by  the  help  of  the  map. 

It  may  be  regarded  as  a  canonization  of  "  Divine  Geometry,"  but 
has  no  special  mythological  legend  connected  with  it. 

38.  Aries,   the   Ram   (Map   II).      December.  —  This   is 
the  second  of  the  zodiacal  constellations,  now  occupying 
the  sign  of  Taurus.     It  lies  just  south  of  Triangulum  and 
Perseus.     Its  characteristic  star-group  is  that  composed  of 
Alpha  (Hamal],  Beta,  and  Gamma  (see  map),  about  20°  due 
south  of  Gamma  Andromedse.     Alpha,  a  star  of  2£  mag- 
nitude, is  fairly  conspicuous,  forming  a  large  isosceles  tri- 
angle with  Beta  and  Gamma  Andromedse. 

Gamma  Arietis  is  a  very  pretty  double  star  with  the  components 
about  9"  apart.  It  is  probably  the  first  double  star  discovered, 
having  been  noticed  by  Hooke  in  1664. 

The  star  41  Arietis  (3£  magnitude),  which  forms  a  nearly  equilat- 
eral triangle  with  Alpha  Arietis  and  Gamma  Trianguli,  constitutes, 
with  two  or  three  other  stars  near  it,  the  constellation  of  Musca 
(Borealis),  a  constellation,  however,  not  now  generally  recognized. 

According  to  the  Greeks,  Aries  is  the  ram  which  bore  the  Golden 
Fleece  and  dropped  Helle  into  the  Hellespont,  when  she  and  her 
brother,  Phrixus,  were  fleeing  on  its  back  to  Colchis.  Long  after- 
wards the  Argonautic  Expedition,  with  Jason  as  its  head  and  Her- 
cules as  one  of  its  members,  sailed  from  Greece  to  Colchis  to  recover 
the  fleece,  and  finally  succeeded  after  long  endeavors. . 

39.  Cetus,   the    Sea-Monster   (Map   II).     November  to 
December.  —  South  of  Aries  and  Pisces  lies  the  huge  con- 
stellation of  Cetus,  the  sea-monster,  which  backs  up  into 
the  sky  from  the  southeastern  horizon.     The   head  lies 
some  20°  southeast  of  Alpha  Arietis,  and  is  marked  by  an 
irregular  five-sided  figure  of  stars,  each  side  being  some 


URANOGRAPHY  3T 

5°  or  6°  long.  The  southern  edge  of  this  pentagon  is- 
formed  by  the  stars  Alpha,  or  Menkar  (2i  magnitude),  and 
Gamma  (3i  magnitude) ;  Delta  lies  southwest  of  Gamma. 
Beta  (Deneb  Ceti),1  the  brightest  star  of  the  constellation 
(2  magnitude),  stands  by  itself  nearly  40°  west  and  south 
of  Alpha.  Gamma  is  a  very  pretty  double  star,  but  rather 
close  for  a  small  telescope,  the  components  being  only 
2".5  apart,  yellow  and  blue. 

Cetus  is  the  leviathan  that  was  sent  by  Neptune  to  ravage  Libya 
and  devour  Andromeda.  Perseus  turned  him  into  stone  by  showing 
him  the  head  of  the  Gorgon,  Medusa.  On  the  globes  he  is  usually 
represented  as  a  nondescript  sort  of  beast,  with  a  face  like  a  puppy's, 
and  a  tightly  curled  tail;  as  if  the  Gorgon's  head  had  frightened 
out  all  his  savageness. 

South  of  Cetus  lies  the  modern  constellation  of  Sculptoris  Appa- 
ratus (usually  known  simply  as  Sculptor),  which,  however,  contains 
nothing  that  requires  notice  here.  South  of  Sculptor,  and  close  to 
the  horizon,  even  when  on  the  meridian,  is  Phoenix.  It  has  some 
bright  stars,  but  none  easily  observable  in  the  United  States. 

40.  Perseus  (Maps  I  and  II) .  January.  —  Returning 
now  to  the  northern  limit  of  the  map,  we  come  to  the  con- 
stellation of  Perseus.  Its  principal  star  is  Alpha  (Algenib), 
rather  brighter  than  the  standard  second  magnitude,  and 
situated  very  nearly  on  the  prolongation  of  the  line  of  the 
three  chief  stars  of  Andromeda.  A  very  characteristic 
configuration  is  the  so-called  "  segment  of  Perseus " 
(Map  I),  a  curved  line  formed  by  Delta,  Alpha,  Gamma, 
and  Eta,  with  some  smaller  stars,  concave  towards  the 
northeast,  and  running  along  the  line  of  the  Milky  Way 
towards  Cassiopeia.  The  remarkable  variable  star,  Beta, 
or  Algol,  is  situated  about  9°  south. and  a  little  west  of 

1  Deneb  signifies  "tail,"  and  there  are  several  stars  of  that  name. 


38  LESSONS  IN  ASTRONOMY 

Alpha,  at  the  right  angle  of  a  right-angled  triangle  which 
it  forms  with  Alpha  Persei  and  Gamma  Andromedse. 
Algol  and  a  few  small  stars  near  it  form  "Medusa's 
Head,"  which  Perseus  carries  in  his  hand.  (For  further 
particulars  and  recent  discoveries  regarding  this  star,  see 
Sees.  358  and  360.) 

In  this  constellation,  nearly  in  the  center  of  the  triangle 
formed  by  Algenib  with  Algol  and  Epsilon,  appeared  the 
remarkable  temporary  star,  or  Nova^  of  1901,  the  most 
brilliant  of  its  kind  for  nearly  300  years.  (See  Sec.  355*.) 

Epsilon  is  a  very  pretty  double  star  with  the  components  about 
80"  apart ;  but  the  most  beautiful  telescopic  object  in  the  constel- 
lation, perhaps  the  finest  indeed  in  the  whole  heavens  for  a  small 
telescope,  is  the  pair  of  clusters  about  half-way  between  Gamma 
Persei  and  Delta  Cassiopeise,  visible  to  the  naked  eye  as  a  bright 
knot  in  the  Milky  Way,  and  already  referred  to  in  Sec.  32. 

Perseus  was  the  son  of  Danae  by  Jupiter,  who  won  her  in  a 
shower  of  gold.  He  was  sent  by  his  enemies  on  the  desperate 
venture  of  capturing  the  head  of  Medusa,  the  only  mortal  one  of 
the  three  Gorgons,  which  were  frightful  female  monsters  with  wings, 
tremendous  claws,  and  brazen  teeth,  and  serpents  for  hair  j  of  such 
aspect  that  the  sight  turned  to  stone  all  who  looked  at  them.  The 
gods  helped  Perseus  by  various  gifts,  which  enabled  him  to  approach 
his  victim,  invisible  and  unsuspected,  and  to  deal  the  fatal  blow 
without  looking  at  the  sight  himself.  From  the  blood  of  Medusa, 
where  her  body  fell,  sprang  Pegasus,  the  winged  horse,  and  where 
the  drops  fell  on  the  sands  of  Libya,  as  Perseus  was  flying  across 
the  desert,  thousands  of  venomous  serpents  swarmed.  On  his  way, 
returning  home,  he  saw  and  rescued  Andromeda,  as  already  men- 
tioned (Sees.  28  and  35).  Hercules  was  one  of  their  descendants. 

41.  Auriga,  the  Charioteer  (Maps  I  and  II).  January.  — 
Proceeding  east  from  Perseus  we  come  to  Auriga,  who  is 
represented  as  holding  in  his  arms  a  goat  and  her  kids. 


URANOGRAPHY  39 

The  constellation  is  instantly  recognized  by  the  bright 
yellow  star  Capella  (the  Goat)  and  her  attendant  "  Hcedi " 
(the  Kids).  Alpha  Aurigse  (Capella)  is,  according  to 
Pickering,  precisely  of  the  same  brightness  as  Vega,  both 
of  them  being  about  £  of  a  magnitude  fainter  than  Arc- 
turus,  but  distinctly  brighter  than  any  other  stars  visible 
in  our  latitudes  except  Sirius  itself.  The  spectroscope 
shows  that  Capella  is  very  similar  in  character  to  our  own 
sun,  though  probably  vastly  larger.  It  has  recently  been 
discovered  to  be  a  spectroscopic  binary  like  Mizar  (Sec.  26). 
About  10°  east  of  Capella  is  Beta  Aurigse  (Menkalinari) 
of  the  second  magnitude;  Epsilon,  Zeta,  and  Eta,  which 
form  a  long  triangle  4°  or  5°  south  of  Alpha,  are  the  Kids. 

There  seems  to  be  no  well-settled  mythological  history  for  this  con- 
stellation, though  some  say  that  he  is  the  charioteer  of  (Enomaus, 
king  of  Elis ;  while  others  connect  him  with  the  story  of  Phaethon, 
the  son  of  Apollo,  who  borrowed  the  horses  of  his  father  and  was 
overthrown  in  mid-heaven.  The  goat  is  supposed  to  be  Amalthea, 
the  goat  which  suckled  Jupiter  in  his  infancy.  Capella  and  the 
Kids  were  always  regarded  by  astrologers  as  of  kindly  influence, 
especially  towards  sailors. 

42.  Taurus,  the  Bull  (Map  II).  January.  —  This,  the 
third  of  the  zodiacal  constellations,  lies  directly  south  of 
Perseus  and  Auriga,  and  north  of  Orion.  It  is  unmistak- 
ably characterized  by  the  Pleiades,  and  by  the  Y-shaped 
group  of  the  Hyades  which  forms  the  face  of  the  bull, 
with  the  red  Aldebaran  (Alpha  Tauri),  a  standard  first- 
magnitude  star,  blazing  in  the  creature's  eye,  as  he  charges 
down  upon  Orion.  His  long  horns  reach  out  towards 
Gemini  and  Auriga,  and  are  tipped  with  the  second-  and 
third-magnitude  stars,  Beta  and  Zeta.  As  in  the  case  of 


40  LESSONS  IN  ASTRONOMY 

Pegasus,  only  the  head  and  shoulders  appear  in  the  con- 
stellation. Six  of  the  Pleiades  are  easily  visible,  and  on 
a  dark  night  a  fairly  good  eye  will  count  nine  of  them. 
With  a  three-inch  telescope  about  one  hundred  stars  are 
visible  in  the  cluster,  which  is  more  fully  described  with  a 
figure  in  Sec.  376.  The  brightest  of  the  Pleiades  is  called 
Alcyone,  and  was  assigned  to  the  dignity  of  the  "  Central 
Sun  "  by  Maedler  (Sec.  386). 

About  1°  west  and  a  little  north  of  Zeta  is  a  nebula  (Messier  1), 
which  has  many  times  been  discovered  by  tyros  with  a  small  tele- 
scope as  a  new  comet ;  it  is  an  excellent  imitation  of  the  real  thing. 

According  to  the  Greek  legends,  Taurus  is  the  milk-white  bull 
into  which  Jupiter  changed  himself  when  he  carried  away  Europa 
from  Phoenicia  to  the  island  of  Crete,  where  she  became  the  mother 
of  Minos  and  the  grandmother  of  Deucalion,  the  Noah  of  Greek 
mythology.  But  Taurus,  like  most  of  the  other  zodiacal  constel- 
lations, is  really  far  older  than  the  Greek  mythology,  and  appears 
in  the  most  ancient  zodiacs  of  Egypt,  where  it  was  probably  con- 
nected with  the  worship  of  the  bull,  Apis;  so  also  in  the  ancient 
Astronomy  of  Chaldea  and  India. 

The  Pleiades  were  daughters  of  the  giant  Atlas.  Of  .the  seven 
sisters,  one,  who  married  a  mortal,  lost  her  brightness,  according  to 
the  legend,  so  that  only  six  remain  visible.  Some  say  that  Merope 
was  the  one  who  thus  gave  up  her  immortality  for  love,  but  her  star 
is  still  visible,  while  Celseno  and  Asterope  are  both  faint.  The  now 
recognized  names  of  the  stars  in  the  group  (see  map,  Sec.  376) 
include  Atlas  and  Pleione,  the  parents  of  the  family,  as  well  as  the 
seven  sisters.  As  for  the  Hyades,  who  were  half-sisters  of  the 
Pleiades,  there  is  less  legendary  interest  in  their  case.  They  are 
always  called  by  the  poets  the  "  rainy  Hyades." 

43.  Orion  (not  O'rion)  (Map  II).  February.  —  This  is 
the  most  splendid  constellation  in  the  heavens.  As  the 
giant  stands  facing  the  bull,  his  shoulders  are  marked  by 


URANOGRAPHY  41 

the  two  bright  stars  Alpha  (Betelgeuze,  pronounced  BStel- 
jeuze)  and  Gamma  (JBellatrix),  the  former  of  which  in  color 
closely  matches  Aldebaran,  though  its  brightness  is  some- 
what variable.  In  his  hand  he  holds  up  the  lion  skin, 
indicated  by  the  curved  line  of  little  stars  between  Gamma 
and  the  Hyades.  The  top  of  the  club,  which  he  brandishes, 
lies  between  Zeta  Tauri  and  Mu  and  Eta  Geminorum.  His 
head  is  marked  by  a  little  triangle  of  stars  of  which  Lambda 
is  the  chief.  His  belt,  through  the  northern  end  of  which 
passes  the  celestial  equator,  consists  of  three  stars  of  the 
second  magnitude,  pointing  obliquely  southeast  toward 
Sirius.  It  is  very  nearly  3°  in  length,  and  is  known  in  Eng- 
land as  the  "  Ell  and  Yard."  From  the  belt  hangs  the  sword, 
composed  of  three  smaller  stars  lying  more  nearly  north  and 
south;  the  middle  one  of  them  is  the  multiple,  Theta,  in  the 
great  nebula,  which  even  in  a  small  telescope  is  a  beautiful 
object,  the  finest  nebula  in  the  sky.  (See  Fig.  94,  Sec.  378.) 
Beta  Orionis,  or  Rigel,  a  magnificent  white  star,  is  in  one  of 
his  feet,  and  Kappa  is  in  the  knee  of  the  other  leg.  (Orion 
has  only  one  foot,  or  if  he  has  another  it  is  hidden  behind 
Lepus.)  The  quadrilateral  Alpha,  Gamma,  Beta,  Kappa, 
with  the  diagonal  belt,  Delta,  Eta,  Zeta,  once  learned  can 
never  be  mistaken  for  anything  else  in  the  heavens. 

Rigel  is  a  very  pretty  double  star,  the  larger  star  having  a  very 
small  companion  about  10"  distant.  The  two  stars  at  the  extremities 
of  the  belt  are  also  double. 

Orion  was  a  giant  and  mighty  hunter,  son  of  Neptune,  and  beloved 
by  both  Aurora  and  Diana.  The  legends  of  his  life  and  exploits  are 
numerous,  and  often  contradictory.  He  conquered  every  creature 
except  the  Scorpion,  which  stung  and  killed  him.  As  a  winter  con- 
stellation his  influence  was  counted  stormy,  and  he  was  greatly 
dreaded  by  sailors. 


42  LESSONS  IN  ASTRONOMY 

44.  Eridanus,  the  River  Po  (Map  II).     January. — This  constel- 
lation lies  south  of  Taurus,  in  the  space  between  Cetus  and  Orion, 
and  extends  far  below  the  southern  horizon.     The  portion  near  the 
south  pole  has  a  pair  of  bright  stars,  which,  of  course,  are  never  visible 
at  the  United  States.     Starting  with  Beta  (Cursa,  as  it  is  called), 
of  the  third  magnitude,  about  3°  north  and  a  little  west  of  Rigel,  one 
can  follow  a  sinuous  line  of  stars  westward  to  the  paws  of  Cetus, 
where  the  stream  turns  at  right  angles  and  runs  southward  and 
southwest  to  the  horizon.     To  trace  it  conveniently,  however,  requires 
a  map  on  a  larger  scale  than  the  one  we  present. 

45.  Lepus  and  Columba  (Map  II).    February.  —  The  con- 
stellation of  Lepus  (the  Hare),  one  of  Orion's  victims,  is  one 
of  the  ancient  forty-eight,  and  lies  just  south  of  the  giant, 
occupying  a  space  of  some  15°  square.     Its  characteristic 
configuration  is  a  quadrilateral  of  third-  and  fourth-magni- 
tude stars,  with  sides  from  3°  to  5°  long,  about  10°  south 
of  Kappa  Orionis,  and  15°  west  of  Sirius. 

.  Columba,  the  Dove,  lies  next  south  of  Lepus,  too  far 
south  to  be  well  seen  in  the  Northern  States.  Its  principal 
star,  Alpha  (Phact),  is  of  2£  magnitude,  and  is  readily  found 
by  drawing  a  line  from  Procyon  to  Sirius  and  prolonging 
it  about  the  same  distance.  In  passing,  we  may  note  that 
a  similar  line  drawn  from  Alpha  Orionis  through  Sirius, 
and  produced,  will  strike  near  Zeta  Argus,  or  Naos,  a  star 
about  as  bright  as  Phact,  —  the  two  lines  which  intersect 
at  Sirius  making  the  so-called  "  Egyptian  X." 

Columba  is  a  modern  constellation,  commemorating  Noah's  dove 
returning  to  the  ark  with  the  olive  branch. 

46.  Lynx  (Maps  I,  II,  and  III).     February.  —  Returning  now 
to  the  northern  limit  of  the  map,  we  find  the  modern  constellation 
of  the  Lynx  lying  just  east  of  Auriga,  and  enveloping  it  on  the  north 
and  in  the  circumpolar  region,  as  shown  on  the  map.     It  contains 


URANOGRAPHY  43 

no  stars  above  the  fourth  magnitude,  and  is  of  no  importance  except 
as  occupying  an  otherwise  vacant  space. 

47.  Gemini,  the  Twins  (Map  II).     February  and  March. 

—  This  is  the  fourth  of  the  zodiacal  constellations,  now 
lying  mostly  in  the  sign  of  Cancer.  It  contains  the  sum- 
mer solstitial  point  —  the  point  where  the  sun  turns  from 
its  northern  motion  to  its  southern  in  the  summer.  At 
present  it  is  about  2°  west  and  a  little  north  of  the  star 
Eta.  Gemini  lies  northeast  of  Orion  and  southeast  of 
Auriga,  and  is  sufficiently  characterized  by  the  two  stars 
Alpha  and  Beta  (about  4£°  apart),  which  mark  the  heads 
of  the  twins.  The  southern  one,  Beta,  or  Pollux,  is  now 
the  brighter;  but  Alpha  (Castor)  is  much  more  interesting, 
as  being  double  (easily  seen  with  a  small  telescope).  The 
feet  are  marked  by  the  third-magnitude  stars  Gamma  and 
Mu,  some  10°  east  of  Zeta  Tauri. 

Castor  and  Pollux  were  the  sons  of  Jupiter  by  Leda,  and  ancient 
mythology,  especially  that  of  Rome,  is  full  of  legends  relating  to 
them.  Many  of  our  readers  will  remember  Macaulay's  ballad  of  "  The 
Battle  of  Lake  Regillus,"  when  they  won  the  fight  for  Rome.  They 
were  regarded  as  the  special  patrons  of  the  sailor,  who  relied  much  on 
their  protection  against  the  evil  powers  of  Orion  and  the  Hyades. 

48.  Canis  Minor,  the  Little  Dog  (Map  III).     March. — 
This  constellation,  about  20°  south  of  Castor  and  Pollux, 
is  marked  by  the  bright  star  Procyon,  which  means  "  before 
the  dog,"  because  it  rises  about  half  an  hour  before  the 
Dog  Star  (Sirius).     Alpha,  Beta,  and  Gamma  form  together 
a  configuration  closely  resembling  that  formed  by  Alpha, 
Beta,  and  Gamma  Arietis.     Procyon,  Alpha  Orionis,  and 
Sirius  form   a  nearly  equilateral  triangle,  with  sides   of 
about  25°. 


44  LESSONS  IN  ASTRONOMY 

The  animal  is  supposed  to  have  been  one  of  Orion's  dogs,  though 
some  say  the  dog  of  Icarus,  whom  they  identify  with  Bootes. 

49.  Canis  Major,  the  Great  Dog  (Map  II).     February.— 
This  glorious  constellation  hardly  needs  description.     Its 
Alpha  is  the  Dog  Star  (Sirius),  beyond  all  comparison  the 
brightest  star  in  the  heavens,  and  one  of  our  nearer  neigh- 
bors, —  so  distant,  however,  that  it  requires  more   than 
eight  years  for  light  to  come  to  us  from  it.     It  is  nearly 
pointed  at  by  a  line   drawn  through  the  three  stars  at 
Orion's  belt.     Beta,  at  the  extremity  of  the  uplifted  paw, 
is  of  the  second  magnitude,  and  so  are  several  of  the  stars 
farther  south  in  the  rump  and  tail  of  the  animal,  who  sits 
up  watching  his  master  Orion,  but  with  an  eye  out  for 
Lepus. 

50.  Monoceros,  the  Unicorn  (Map  II).     March.  —  This  is  one  of 
the  modern  constellations  organized  by  Hevelius   to  fill  the   gap 
between  Gemini  and  Canis  Minor  on  the  north,  and  Argo  Navis  and 
Canis  Major  on  the  south.     It  lies  just  east  of  Orion  and  has  no 
conspicuous  stars,  but  is  traversed  by  a  brilliant  portion  of  the  Milky 
Way.    The  Alpha  of  the  constellation  (fourth  magnitude)  lies  about 
half-way  between  Alpha  Orionis  and  Sirius,  a  little  west  of  the  line 
that  joins  them.     11,  or  Alpha,  Monocerotis,  a  fine  triple  star  (see 
Fig.  88,  Sec.  366),  fourth  magnitude,  is  very  nearly  pointed  at  by  a 
line  drawn  from  Zeta  Canis  Majoris  northward  through  Beta,  and 
continued  as  far  again. 

51.  Argo  Navis,  the  Ship  Argo  (genitive  Argus)  (Maps  II 
and  III).     March.  —  This  is  one  of  the  largest,  oldest,  and 
most  important  of  the  constellations,  lying  south  and  east 
of  Canis  Major.    Its  brightest  star,  Alpha  Argus  (Canopus), 
ranks  next  to  Sirius  and  is  visible  in  the  Southern  States, 
but  not  in  the  Northern.     The  constellation,  huge  as  it  is, 
is  only  a  half  one,  like  Pegasus  and  Taurus,  —  only  the 


UBAISTOGRAPHY  45 

stern  of  a  vessel,  with  mast,  sail,  and  oars ;  the  stem  being 
wanting.  In  the  part  of  the  constellation  covered  by  our 
maps  there  are  no  very  conspicuous  stars,  though  there  are 
some  of  third  and  fourth  magnitude  which  lie  east  and 
southeast  of  the  rump  and  tail  of  Canis  Major.  We  have 
already  mentioned  Zeta,  or  Naos,  at  the  southeast  extremity 
of  the  «  Egyptian  X." 

The  constellation  is  so  large  that  for  convenience  it  has  recently 
been  divided  into  four  sub-constellations,  Mains  (the  mast),  Vela 
(the  sails),  Puppis  (the  stern),  and  Carina  (the  keel  or  hull).  This 
new  division  sometimes  leads  to  misunderstanding ;  thus  Eta  Carinse 
is  not  always  at  first  recognized  as  the  Eta  Argus  of  older  astronomers. 

According  to  the  Greek  legends,  this  is  the  miraculous  ship  in 
which  Jason  and  his  fifty  companions  sailed  from  Greece  to  Colchis 
to  recover  the  Golden  Fleece.  It  had  in  its  bow  a  piece  of  oak  from 
the  sacred  grove  of  Dodona,  which  enabled  the  ship  to  talk  with  its 
commander  and  give  him  advice. 

Some  see  in  the  constellation  the  ark  of  Noah. 

52.  Cancer,  the  Crab  (Maps  II  and  III).  March.  —  This 
is  the  fifth  of  the  zodiacal  constellations,  lying  just  east  of 
Canis  Minor.  It  does  not  contain  a  single  conspicuous 
star,  but  is  e-asily  recognizable  from  its  position,  and  in  a 
dark  night  by  the  nebulous  cloud  known  as  Prcesepe,  or  the 
"  Manger,"  with  the  two  stars  Gamma  and  Delta  near  it, 
-the  so-called  Aselli,  or  "Donkeys."  Prsesepe,  some- 
times also  called  the  "  Beehive,"  is  really  a  coarse  cluster  of 
seventh-  and  eighth-magnitude  stars,  resolvable  by  an  opera- 
glass.  The  line  from  Castor  through  Pollux,  produced 
about  12°,  passes  near  enough  to  it  to  serve  as  a  pointer. 

The  star  Zeta  is  a  very  pretty  triple  star,  though  with  a  small  tel- 
escope it  can  be  seen  only  as  double.  It  is  easily  found  by  a  line 
from  Castor  through  Pollux,  produced  2£  times  as  far. 


46  LESSONS  IN  ASTRONOMY 

By  the  Greeks  this  was  identified  as  the  Crab  who  attacked 
Hercules  when  he  was  fighting  the  Lernaean  Hydra.  In  the  old 
Egyptian  zodiacs  the  Crab  is  replaced  by  the  Scarabaeus,  or  Beetle ; 
and  in  some  of  the  more  recent  zodiacs  by  a  pair  of  asses,  still 
recognized  in  the  name  Aselli,  given  to  the  two  stars  Gamma 
and  Delta. 

53.  Leo,  the  Lion  (Map  III).    April East  of  Cancer 

lies  the  noble  constellation  of  Leo,  which  adorns  the  even- 
ing sky  in  March  and  April ;  it  is  the  sixth  of  the  zodiacal 
constellations,  now  occupying  the  sign  of  Virgo.     Its  lead- 
ing star,  Regulus,  or  "  Cor  Leonis,"  is  of  the  first  magni- 
tude, and  two  others,  Beta  (Denebola)  and  Gamma,  are  of 
the  second  magnitude.     Alpha,  Gamma,  Delta,  and  Beta 
form  a  conspicuous  irregular  quadrilateral  (see  map),  the 
line  from  Regulus  to  Denebola  being  about   26°  long. 
Another  characteristic  configuration  is  the   "  Sickle,"  of 
which  Regulus  is  the  handle,  and  the  curved  line  Eta, 
Gamma,  Zeta,  Mu,  and  Epsilon  is  the  blade,  the  cutting 
edge  being  turned  towards  Cancer. 

The  "  radiant "  of  the  November  meteors  lies  between  Zeta  and 
Epsilon.  Gamma,  in  the  Sickle,  and  at  the  southeast  corner  of  the 
quadrilateral,  is  a  very  pretty  double  star  —  binary  —  with  a  period 
of  about  400  years. 

According  to  classic  writers,  this  is  the  Nemsean  Lion  which  was 
killed  by  Hercules,  as  the  first  of  his  Twelve  Labors ;  but,  like  Aries 
and  Taurus,  the  constellation  is  far  older  than  the  Greeks  and  stands 
in  its  present  form  on  all  the  ancient  zodiacs. 

54.  Leo  Minor  and  Sextans  (Map  III).    April.— Leo  Minor 
(the  Smaller  Lion)  is   an   insignificant   modern  constellation   com- 
posed of  a  few  small  stars  north  of  Leo,  between  it  and  the  feet 
of  Ursa  Major.     It  contains  nothing  deserving  special  notice.     The 
same  remark  holds  good  as  to  Sextans  (the  Sextant),  and  even  more 
emphatically. 


URANOGRAPHY  47 

55.  Hydra  (Map  III).  March  to  June.  —  This  constel- 
lation, with  its  riders,  Crater  (the  Cup)  and  Corvus  (the 
Raven),  is  a  large  and  important  one,  though  not  very 
brilliant.  The  head  is  marked  by  a  group  of  five  or  six 
fourth-  and  fifth-magnitude  stars  just  15°  south  of  Prsesepe. 
A  curving  line  of  small  stars  leads  down  southeast  to 
Alpha,  Cor  Hydrce,  or  Alphard  (which  means  "the  soli- 
tary"), a  2£-magnitude  star  standing  very  much  alone. 
From  there,  as  the  map  shows,  an  irregular  line  of  fourth- 
magnitude  stars  running  far  south  and  then  east,  almost 
to  the  boundary  of  Scorpio,  marks  the  creature's  body  and 
tail,  the  whole  extending  very  nearly  90°.  About  the 
middle  of  the  length  of  Hydra,  and  just  below  the  hind 
feet  of  Leo  (30°  due  south  from  Denebola),  we  find  the 
little  constellation  of  Crater;  and  just  east  of  it  the  still 
smaller  but  much  more  conspicuous  one  of  Corvus,  with 
two  second-magnitude  stars  in  it,  and  four  of  the  third 
and  fourth  magnitudes.  It  is  well  marked  by  a  character- 
istic quadrilateral  (see  map),  with  Delta  and  Eta  together 
at  its  northeast  corner.  The  order  of  the  letters  in  Corvus 
differs  widely  from  that  of  brightness,  suggesting  that 
changes  may  have  occurred  since  the  letters  were  applied. 

Epsilon  Hydrae  and  Delta  Corvi  are  pretty  double  stars,  the  latter 
easily  seen  with  a  small  telescope ;  colors,  yellow  and  purple. 

Hydra,  according  to  the  Greeks,  is  the  immense  hundred-headed 
monster  which  inhabited  the  Lernsean  Marsh,  and  was  killed  by  Her- 
cules as  his  second  labor.  But  the  Hydra  of  the  heavens  has  only 
one  head,  and  is  probably  much  older  than  the  legends  of  Hercules. 

An  old  legend  says  that  Corvus  is  Coronis,  a  nymph  who  was 
transformed  into  a  raven  to  escape  the  pursuit  of  Neptune.  Another 
story  is  that  she  was  changed  into  a  crow  for  telling  tales  of  some 
imprudent  actions  of  Jupiter  which  came  under  her  notice. 


48  LESSONS  IN  ASTRONOMY 

56.  Virgo  (Map  III).     May.  —  East  and  south  of  Leo 
lies  Virgo,  the  seventh  zodiacal  constellation,  mostly  in 
the  sign  of  Libra.     Its  Alpha  (Spica  Virginis)  is  of  the 
1J   magnitude   and,  standing  rather  alone,  10°  south  of 
the  celestial  equator,  is  easily  recognized  as  the  southern 
apex  of  a  nearly  equilateral  triangle  which  it  forms  with 
Denebola  (Beta  Leonis)  to  the  northwest,  and  Arcturus 
northeast  of  it.     Beta  Virginis,  of  the  third  magnitude,  is 
14°  south  of  Denebola.    A  line  drawn  eastward  and  a  little 
south  from  Beta  (third  magnitude)  and  then  carried  on, 
curving  northward,  passes  successively  (see  map)  through 
Eta,  Gamma,  Delta,  and  Epsilon,  of  the  third  magnitude. 
(Notice  the  word  "  Begde,"  like  "  Bagdei  "  in  Cassiopeia, 
Sec.  28.) 

Gamma  is  a  remarkable  binary  star,  at  present  easily  visible  as 
double  in  a  small  telescope.  Its  period  is  185  years,  and  it  has 
completed  pretty  nearly  a  full  revolution  since  its  first  discovery. 
(For  a  diagram  of  its  orbit,  see  Fig.  89,  Sec.  369.)  A  few  degrees 
north  of  Gamma  lies  the  remarkable  nebulous  region  of  Virgo,  con- 
taining hundreds  of  these  curious  objects;  but  for  the  most  part 
they  are  very  faint,  and  observable  only  with  large  telescopes. 

The  classic  poets  recognize  Virgo  as  Astrsea,  the  goddess  of  jus- 
tice, who,  last  of  all  the  old  divinities,  left  the  earth  at  the  close  of 
the  Golden  Age.  She  holds  the  Scales  of  Justice  (Libra)  in  one  hand, 
and  in  the  other  a  sheaf  of  wheat. 

Some  identify  her  with  Erigone,  the  daughter  of  Icarus  or  Bootes. 
Others  recognize  in  her  the  Egyptian  Isis. 

57.  Coma  Berenices,  Berenice's  Hair  (Map  III).     May.  —  This 
little  constellation,  composed  of  a  great  number  of  fifth-  and  sixth- 
magnitude  stars,  lies  30°  north  of  Gamma  and  Eta  Virginis,  and  about 
15°  northeast  of  Denebola.      It  contains  a  number  of  interesting 
double  stars,  but  they  are  not  easily  found  without  the  help  of  a 
telescope  equatorially  mounted. 


URANOGRAPHY  49 

The  constellation  was  established  by  the  Alexandrian  astronomer 
Conon,  in  honor  of  the  queen  of  Ptolemy  Soter.  She  dedicated  her 
splendid  hair  to  the  gods,  to  secure  her  husband's  safety  in  war. 

58,  Canes  Venatici,  the  Hunting-Dogs  (Map  III).    May.- 
These  are  the  dogs  with  which  Bootes,  the  huntsman,  is 
pursuing  the  Great  Bear  around  the  pole ;  the  northern  of 
the  two  is  Asterion,  the  southern  Char  a.     Most  of  the  stars 
are  small,  but  Alpha  is  of  the  2^-  magnitude,  and  is  easily 
found  by  drawing  from  Eta  Ursse  Majoris  (the  star  in  the 
end  of  the  Dipper-handle)  a  line  to  the  southwest,  perpen- 
dicular to  the  line  from  Eta  to  Zeta  (Mizar),  and  about 
15°  long;  in  England  it  is  generally  known  as  Cor  Caroli 
(the  Heart  of  Charles),  in  allusion  to  Charles  I.     With 
Arcturus  and  Denebola  it  forms  a  triangle  much  like  that 
which  they  form  with  Spica. 

The  remarkable  whirlpool  nebula  of  Lord  Rosse  is  situated  in  this 
constellation,  about  3°  west  and  somewhat  south  of  the  star  Eta 
Ursse  Majoris.  In  a  small  telescope  it  is  by  no  means  conspicuous, 
but  in  a  large  telescope  is  a  wonderful  object. 

The  constellation  is  modern,  formed  by  Hevelius. 

59.  Bootes,  the  Huntsman  (Maps  I  and  III).     June.— 

This  fine  constellation  extends  more  than  60°  in  declina- 
tion, from  near  the  equator  quite  to  Draco,  where  the 
uplifted  hand  holding  the  leash  of  the  hunting-dogs  over- 
laps the  tail  of  the  Bear.  Its  principal  star,  Alpha  (Arctu- 
rus, meaning  "bear-driver"),  is  of  a  ruddy  hue,  and  in 
brightness  is  excelled  only  by  Sirius  among  the  stars  visible 
in  our  latitudes.  It  is  at  once  recognizable  by  its  forming 
with  Spica  and  Denebola  the  great  triangle  already  men- 
tioned (Sec.  56).  Six  degrees  west  and  a  little  south  of  it 
is  Eta,  of  the  third  magnitude,  which  forms  with  it,  in 


50  LESSONS  IN  ASTRONOMY 

connection  with  Upsilon,  a  configuration  like  that  in  the 
head  of  Aries.  Epsilon  is  about  10°  northeast  of  Arcturus, 
and  in  the  same  direction  about  1 0°  farther  lies  Delta.  The 
map  shows  the  pentagon  which  is  formed  by  these  two  stars 
along  with  Beta,  Gamma,  and  Rho. 

Epsilon  is  a  fine  double  star ;  colors,  orange  and  greenish  blue ; 
distance,  about  3". 

The  legendary  history  of  this  constellation  is  very  confused.  One 
legend  makes  it  to  be  Icarus,  the  father  of  Erigone  (Virgo),  but  the 
one  most  usually  accepted  makes  it  to  be  Areas,  son  of  Callisto.  After 
she  was  changed  to  a  bear  (Ursa  Major),  her  son,  not  recognizing 
her,  hunted  her  with  his  dogs,  "and  was  on  the  point  of  killing  her, 
when  Jupiter  interfered  and  took  them  both  to  the  stars. 

60.  Corona   Borealis,   the   Northern  Crown   (Map  III). 
June.  —  This  beautiful  little  constellation  lies  20°  north- 
east of  Arcturus,  and  is  at  once  recognizable  as  an  almost 
perfect  semicircle  composed  of  half  a  dozen  stars,  among 
which  the  brightest,  Alpha  (G-emma,  or  Alphaccci),  is  of  the 
second  magnitude.     The  extreme  northern  one  is  Theta; 
next  comes  Beta,  and  the  rest  follow  on  the  Bagdei  order, 
just  as  in  Cassiopeia.     About  a  degree  north  of  Delta,  now 
visible  with  an  opera-glass,  is  a  small  star  which  in  1866 
suddenly  blazed  out  until  it  became  brighter  than  Alphacca 
itself.     (See  Sec.  355.) 

The  little  star  Eta  is  a  rapid  binary  with  a  period  of  less  than 
forty-two  years.  At  times  it  can  be  easily  divided  by  a  small 
telescope. 

The  constellation  is  said  to  be  the  crown  that  Bacchus  gave  to 
Ariadne,  before  he  deserted  her  on  the  island  of  Naxos. 

61.  Libra,  the  Balance  (Map  III).    June.  —  This  is  the 
eighth  of  the  zodiacal  constellations,  lying  east  of  Virgo, 


URANOGRAPHY  51 

bounded  on  the  south  by  Centaurus  and  Lupus,  on  the 
east  by  the  upstretched  claw  of  Scorpio,  and  on  the  north 
by  Serpens  and  Virgo.  It  is  inconspicuous,  the  most 
characteristic  figure  being  the  trapezoid  formed  by  the 
lines  joining  the  stars  Alpha,  Iota,  Gamma,  and  Beta. 
Beta,  which  is  the  northern  one,  is  about  30°  due  east 
from  Spica,  while  Alpha  is  about  10°  southwest  of  Beta. 
The  remarkable  variable,  Delta  Librae,  is  4°  west  and  a 
little  north  from  Beta.  Most  of  the  time  it  is  of  the  4£  or 
5  magnitude,  but  runs  down  nearly  two  magnitudes,  to 
invisibility,  once  in  2i  days  ("Algol"  type,  Sec.  358). 

Libra  is  the  Balance  of  Virgo,  the  goddess  of  justice,  and  was  not 
recognized  by  the  classic  writers  as  a  separate  constellation  until  the 
time  of  Julius  Caesar,  the  space  now  occupied  by  Libra  being  then 
covered  by  the  extended  claws  of  Scorpio. 

The  cluster  M.  5,  situated  on  the  extreme  northern  border  of 
the  constellation,  is  remarkable  for  the  number  of  variable  stars  it 
contains  (Sec.  361). 

62.  Antlia,  Centaurus,  and  Lupus  (Map  III).  April  to 
June.  —  These  constellations  lie  south  of  Hydra  and  Libra. 

Antlia  Pneumatica  (the  Air-Pump)  is  a  modern  constellation  of  no 
importance  and  hardly  recognizable  by  the  eye,  having  only  a  single 
star  as  bright  as  the  4|  magnitude. 

Centaurus,  on  the  other  hand,  is  an  ancient  and  exten- 
sive asterism,  containing  in  its  south  (circumpolar)  regions, 
not  visible  in  the  United  States,  two  stars  of  the  first  mag- 
nitude, Alpha  and  Beta.  Alpha  Centauri  stands  next  after 
Sirius  and  Canopus  in  brightness  and,  as  far  as  present 
knowledge  indicates,  is  our  nearest  neighbor  among  the  stars. 
The  part  of  the  constellation  which  becomes  visible  in  our 


52  LESSONS  IN  ASTRONOMY 

latitudes  is  not  especially  brilliant,  though  it  contains  sev- 
eral stars  of  the  2£  and  3  magnitudes  in  the  region  lying 
south  of  Corvus  and  Spica  Virginis. 

Lupus  (the  Wolf),  also  one  of  Ptolemy's  constellations,  lies  due  east 
of  Centaurus  and  just  south  of  Libra.  It  contains  a  considerable 
number  of  third-  and  fourth-magnitude  stars ;  but  it  is  too  low  for 
any  satisfactory  study  in  our  latitudes.  It  is  best  seen  late  in  June. 
These  constellations  contain  numerous  objects  interesting  for  a 
southern  observer,  but  not  observable  by  us. 

The  Centaurs  were  a  fabulous  race,  half  man,  half  horse,  who 
lived  in  Thessaly  and  herded  cattle.  Chiron  was  the  most  distin- 
guished of  them,  the  teacher  of  almost  all  the  Greek  heroes  in  every 
manly  and  noble  art,  and  the  friend  of  Hercules,  by  whom,  however, 
he  was  accidentally  killed.  Jupiter  transferred  him  to  the  stars. 
(See  Sagittarius,  Sec.  72.)  The  wolf  is  represented  as  transfixed  by 
the  Centaur's  spear. 

63,  Scorpio  (or  Scorpius;  genitive  Scorpii),  the  Scorpion 
(Map  IV).  July.  —  This,  the  ninth  of  the  zodiacal  con- 
stellations and  the  most  brilliant  of  them  all,  lies  southeast 
of  Libra,  which  in  ancient  times  used  to  form  its  claws 
(Chelse).  It  is  recognized  at  once  by  the  peculiar  configu- 
ration of  the  stars,  which  resembles  a  boy's  kite,  with  a 
long  streaming  tail  extending  far  down  to  the  south  and 
east,  and  containing  several  pairs  of  stars.  The  principal 
star  of  the  constellation,  Antares,  is  of  the  first  magnitude, 
and  fiery  red  like  the  planet  Mars.  From  this  it  gets  its 
name,  which  means  "the  rival  of  Ares"  (Mars).  Antares 
is  a  very  pretty  double  star,  with  a  beautiful  little  green 
companion  just  to  the  west  of  it,  not  very  easy  to  be  seen, 
however,  with  a  small  telescope.  Beta  (second  magnitude) 
is  in  the  arch  of  the  kite  bow,  about  8°  or  9°  northwest  of 
Antares,  while  the  star  which  Bayer  lettered  as  Gamma 


URANOGRAPHY  58 

Scorpii  is  well  within  Libra,  20°  west  of  Antares.  (There 
is  considerable  confusion  among  uranographers  as  to  the 
boundary  between  the  two  constellations.)  The  other 
principal  stars  of  the  constellation  are  easily  found  on 
the  map. 

Many  of  them  are  of  the  second  magnitude.  One  of  the  finest 
clusters  known,  and  easily  seen  with  a  small  telescope,  is  M.  80, 
which  lies  about  half-way  between  Alpha  and  Beta. 

Mu1  is  one  of  the  most  remarkable  of  the  spectroscopic  binaries 
(Sec.  374),  the  relative  velocity  of  the  two  stems  of  the  pair  being 
about  300  miles  a  second,  and  the  period  of  revolution  only  a  day 
and  ten  hours. 

According  to  the  Greek  mythology,  this  is  the  scorpion  that  killed 
Orion.  It  was  the  sight  of  this  monster  of  the  heavens  that  fright- 
ened the  horses  of  the  sun,  when  poor  Phaethon  tried  to  drive  them 
and  was  thrown  out  of  his  chariot.  Among  astrologers,  the  influence 
of  Scorpio  has  always  been  held  as  baleful  to  the  last  degree. 

64.  Norma  Nilotica,  the  rule  with  which  the  height  of  the  Nile 
was  measured,  lies  west  of  Scorpio,  while  Ara  lies  due  south  of  Eta 
and  Theta.     Both  are  modern  constellations,  small  and  of  no  impor- 
tance in  our  latitudes. 

65.  Ophiuchus  and  Serpens  (Map  IV).     July.  —  Ophiu- 
chus  means  the  "serpent-holder,"  and  probably  refers  to 
the  great  physician  ^Esculapius.     The  hero  is  represented 
as  standing  with  his  feet  on  Scorpio  and  grasping  the 
serpent.    The  two  constellations,  therefore,  are  best  treated 
together.     The  head  of  Serpens  is  marked  by  a  group 
of  small  stars  lying  just  south  of  Corona  and  20°  due 
east  of  Arcturus.     Beta  and  Gamma  are  the  two  brightest 
stars  in  the  group,  their  magnitudes   3£   and  4.     Delta 
lies  6°  southwest  of  Beta,  and  there  the  serpent's  body 
bends    southeast  through  Alpha  and    Epsilon   Serpentis 


54  LESSONS  IN  ASTRONOMY 

(see  map)  to  Delta  and  Epsilon  Ophiuchi  in  the  giant's 
hand.  The  line  of  these  five  stars  carried  upwards  passes 
nearly  through  Epsilon  Bobtis,  and  downwards  through 
Zeta  Ophiuchi.  A  line  crossing  this  at  right  angles,  nearly 
midway  between  Epsilon  Serpentis  and  Delta  Ophiuchi, 
passes  through  Mu  Serpentis  on  the  southwest  and  Lambda 
Ophiuchi  to  the  northeast.  The  lozenge-shaped  figure 
formed  by  the  lines  drawn  from  Alpha  Serpentis  and  Zeta 
Ophiuchi  to  the  two  stars  last  mentioned  is  one  of  the  most 
characteristic  configurations  of  the  summer  sky.  Alpha 
Ophiuchi  (2£  magnitude)  (Ras  Alaghue)  is  easily  recog- 
nizable in  connection  with  Alpha  Herculis,  since  they 
stand  rather  isolated,  about  6°  apart,  on  the  line  drawn 
from  Arcturus  through  the  head  of  Serpens,  and  produced 
as  far  again.  Alpha  Ophiuchi  is  the  eastern  and  the 
brighter  of  the  two,  and  forms  with  Vega  and  Altair  a 
nearly  equilateral  triangle.  Beta  Ophiuchi  lies  about  9° 
southeast  of  Alpha. 

Five  degrees  east  and  a  little  south  of  Beta  are  five  small  stars  in 
the  Milky  Way,  forming  a  V  with  the  point  to  the  south,  much  like 
the  Hyades  of  Taurus.  They  form  the  head  of  the  now  discredited 
constellation,  " Poniatowski's  Bull"  (Taurus  Poniatovii),  proposed  in 
1777,  and  found  in  many  maps.  70  Ophiuchi  (the  middle  star  in 
the  eastern  leg  of  the  V  of  Poniatowski's  Bull)  is  a  very  pretty 
double  star  —  binary  —  with  a  period  of  ninety-three  years.  Just  at 
present  the  star  is  too  close  to  be  resolved  by  a  small  instrument. 

Kepler's  "new  star"  of  1604  was  situated  in  the  left  leg  of 
Ophiuchus,  between  Eta  and  Theta. 

Ophiuchus  is  identified  with  ^Esculapius,  who  was  the  first  great 
physician,  the  son  of  Apollo  and  the  nymph  Coronis,  educated  in  the 
art  of  medicine  by  Chiron,  the  Centaur.  The  serpent  and  the  cock 
were  sacred  to  him  in  his  character  as  a  deity.  But  the  constellation 
is  older  than  the  classic  legends. 


URANOGRAPHY  55 

66.  Hercules  (Maps  I  and  IV).  July This  noble  con- 
stellation lies  next  north  of  Ophiuchus,  between  it  and 
Draco.  The  hero  is  represented  as  resting  on  one  knee, 
with  his  foot  on  the  head  of  Draco,  while  his  head  is  close 
to  that  of  Ophiuchus.  The  constellation  contains  no  stars 
of  the  first  or  even  of  the  second  magnitude,  but  there  are 
a  number  of  the  third.  The  most  characteristic  figure 
is  the  keystone-shaped  quadrilateral  formed  by  the  stars 
Epsilon,  Zeta,  Eta,  with  Pi  and  Rho  together  at  the  north- 
east corner.  It  lies  about  midway  on  the  line  from  Vega 
to  Corona. 

On  its  western  boundary,  a  third  of  the  way  from  Eta  towards 
Zeta,  lies  the  remarkable  cluster,  Messier  13,  —  on  the  whole  the 
finest  of  all  star  clusters  in  the  northern  hemisphere,  —  barely 
visible  to  the  naked  eye  on  a  dark  night.  Alpha  Herculis  (Ras 
Algethi),  in  the  head  of  the  giant,  is  a  very  beautiful  double  star; 
colors,  orange  and  blue ;  distance,  about  5".  It  is  also  notably 
variable,  and  has  a  remarkable  spectrum,  characterized  by  numerous 
dark  bands. 

Hercules,  the  son  of  Jupiter  and  Alcmena  (a  granddaughter  of 
Andromeda),  was  the  Greek  incarnation  of  gigantic  strength.  His 
heroic  actions  and  freaks  occupy  more  space  in  their  mythology  than 
those  of  any  personage  except  Jupiter  himself.  He  was  the  pupil  of 
Chiron,  but  by  the  will  of  Jupiter,  his  father,  was  subjected  to  the 
power  of  Eurystheus,  the  king  of  Tiryns,  for  many  years.  At  his 
bidding  he  performed  the  great  enterprises  known  as  the  Twelve 
Labors  of  Hercules,  for  wThich  we  must  refer  the  reader  to  the  Clas- 
sical Dictionaries.  Among  them  we  have  already  mentioned  the  con- 
quest of  the  Nemaean  Lion  and  of  the  Lernsean  Hydra.  Another 
was  to  bring  from  the  garden  of  the  Hesperides  the  golden  apples 
which  were  guarded  by  the  dragon  that  he  killed,  and  on  which  his 
feet  rest  in  the  sky.  His  last  and  greatest  achievement  was  to  bring 
to  the  earth  the  three-header'  dog,  Cerberus,  the  guardian  of  the 
infernal  regions. 


56  LESSONS  IN  ASTRONOMY 

67.  Lyra   (Map  IV).     August.  —  This   constellation  is 
sufficiently  marked  by  the  great  white  or  blue  star,  Vega, 
one  of  the  finest  stars  in  the  whole  sky,  and  certainly  many 
times  larger  than  our  own  sun.     It  is  attended  on  the  east 
by  two  fourth-magnitude  stars,  Epsilon  and  Zeta,  which 
form  with  it  a  little  equilateral  triangle  having  sides  about 
2°  long.     Epsilon  is  a  double-double  or  quadruple  star. 
A  sharp  eye,  even  unaided  by  a  telescope,  divides  the  star 
into  two,  and  a  large  telescope  splits  each  of  the  compo- 
nents.    It  is  a  very  pretty  object  even  for  a  small  telescope 
(Fig.  88).     Beta  and  Gamma,  of  the  third  magnitude  (Beta 
is  variable),  lie  about  8°  southeast  from  Vega,  2£°  apart. 
(See  Sec.  357.) 

On  the  line  between  Beta  and  Gamma,  one-third  of  the  -way  from 
Beta,  lies  Messier  57,  the  Annular  Nebula,  which  can  be  seen  as  a 
small  hazy  ring  even  by  a  small  telescope,  though  of  course  it  is 
much  more  interesting  with  a  larger  one. 

According  to  the  legends  this  constellation  is  the  lyre  of  Orpheus, 
with  which  he  charmed  the  stern  gods  of  the  lower  world,  and  per- 
suaded them  to  restore  to  him  his  lost  Eurydice. 

68,  Cygnus  (Maps  I  and  IV).     September.  —  This  con- 
stellation lies  due  east  from  Lyra,  and  is  easily  recognized 
by  the  cross  that  marks  it.     The  bright  star  Alpha  (1£ 
magnitude)  is  at  the  top,  and  Beta  (third  magnitude)  at 
the  bottom,  while  Gamma  is  where  the  cross-bar  from  Delta 
to  Epsilon  intersects  the  main  piece,  which  lies  along  the 
Milky  Way  from  the  northeast  to  the  southwest.     Beta 
(Albireo)  is  a  beautiful  double  star,  orange  and  dark  blue, 
—  one  of  the  finest  of  the  colored  pairs  for  a  small  telescope. 
61  Cygni,  which  is  memorable  as  the  first  star  to  have  its 
parallax  determined  (by  Bessel  in  1838),  is  easily  found  by 


URANOGRAPHY  57 

completing  the  parallelogram  of  which  Alpha,  Gamma,  and 
Epsilon  are  the  other  three  corners.  Sigma  and  Tau  form 
a  little  triangle  with  61,  which  is  the  faintest  of  the  three. 
61  is  a  fine  double  star.  Delta  is  also  a  fine  double,  but 
too  difficult  for  an  instrument  of  less  than  six  inches 
aperture. 

According  to  Ovid,  Cygnus  was  a  friend  of  Phaethon's,  who 
mourned  his  unhappy  fate  and  was  changed  to  a  swan.  Others  see 
in  the  constellation  the  swan  in  whose  form  Jupiter  visited  Leda, 
the  mother  of  Castor  and  Pollux  and  of  Helen  of  Troy. 

69.  Vulpecula  et  Anser,   the  Fox  and  the  Goose   (Map  IV). 
September.  —  This  little  constellation  is  one  of  those  originated  by 
Hevelius  and  has  obtained  more  general  recognition  among  astrono- 
mers than  most  of  his  creations.     It  lies  just  south  of  Cygnus  and  is 
bounded  to  the  south  by  Delphinus,  Sagitta,  and  Aquila.     It  has  no 
conspicuous  stars,   but  it  contains    one  very  interesting  telescopic 
object,  —  the  "Dumb-bell  Nebula,"  Messier  27.     It  may  be  found 
on  a  line  from  Gamma  Lyrse  through  Beta  Cygni,  produced  as  far 
again. 

70.  Sagitta    (Map   IV).      August.  — This    little    constellation, 
though  very  inconspicuous,  is  one  of  the  old  forty-eight.     It  lies 
south  of  Vulpecula,  and  the  two  stars  Alpha  and  Beta,  which  mark 
the  feather  of  the  arrow,  lie  nearly  midway  between  Beta  Cygni  and 
Altair,  while  its  point  is  marked  by  Gamma,  5°  farther  east  and 
north.     Beta,  the  middle  star  of  the  shaft  of  the  arrow,  is  a  very 
pretty  double  star ;  distance,  about  8" :  the  larger  star  is  itself  a  close 
double. 

71.  A'quila    (not  Aquila)    (Map    IV).     August.  — This 
constellation  lies  on  the  celestial  equator,  east  of  Ophiu- 
chus  and  north  of  Sagittarius  and  Capricornus.    Its  charac- 
teristic configuration  is  that  formed  by  Alpha  (Altair),  with 
Gamma  to  the  north  and  Beta  to  the  south.     It  lies  about 
20°  south  of  Beta  Cygni  and  forms  a  fine  triangle  with 


58  LESSONS  IN  ASTRONOMY 

Beta  and  Alpha  Ophiuchi.  Altair  is  taken  as  the  standard 
first-magnitude  star.  Of  course  several  of  those  which 
are  ordinarily  called  first  magnitude,  like  Sirius  and  Vega, 
are  very  much  brighter  than  this,  while  others  fall  consid- 
erably below  it. 

Aquila  was  the  bird  of  Jupiter,  which  he  kept  by  the  side  of  his 
throne  and  sent  to  bring  Ganymede  to  him. 

The  southern  part  of  the  region  allotted  to  Aquila  on  our  maps  has 
been  assigned  to  Antinoiis,  which  is  recognized  on  some  celestial 
globes.  The  constellation  existed  even  in  Ptolemy's  time,  but  he 
declined  to  adopt  it.  Hevelius  appropriated  the  eastern  part  of 
Antinotis  for  his  constellation  of  Scutum  Sobieski,  which,  however,  is 
now  seldom  recognized. 

72.  Sagittarius,  the  Archer  (Map  IV).  August.— This, 
the  tenth  of  the  zodiacal  constellations,  contains  no  stars 
of  the  first  magnitude,  but  a  number  of  the  second  and 
third  magnitude,  which  make  it  reasonably  conspicuous. 
The  most  characteristic  configuration  is  the  little  inverted 
"  milk-dipper,"  formed  by  the  five  stars  Lambda,  Phi, 
Sigma,  Tau,  and  Zeta,  of  which  the  last  four  form  the 
bowl,  while  Lambda  (in  the  Milky  Way)  is  the  handle. 
(See  map.)  Delta,  Gamma,  and  Epsilon,  which  form  a 
triangle,  right-angled  at  Delta,  lie  south  and  a  little  west 
of  Lambda,  the  whole  eight  together  forming  a  very  strik- 
ing group.  There  is  a  curious  disregard  of  any  apparent 
principle  in  the  lettering  of  the  stars  of  this  constellation ; 
Alpha  and  Beta  are  stars  not  exceeding  in  brightness  the 
fourth  magnitude,  about  4°  apart  on  a  north  and  south 
line,  and  lying  some  15°  south  and  5°  east  of  Zeta  (see 
map),  while  Sigma  is  now  a  bright  second-magnitude  star, 
strongly  suspected  of  being  irregularly  variable.  The 


URANOGRAPHY  59 

constellation  contains  an  unusual  number  of  known  vari- 
ables. The  Milky  Way  in  Sagittarius  is  very  bright  and 
complicated  in  structure,  full  of  knots  and  streamers  and 
dark  pockets,  and  containing  many  beautiful  and  inter- 
esting objects. 

This  constellation  is  said  by  many  writers  to  commemorate  the 
Centaur,  Chiron,  but  the  same  constellation  appears  on  the  ancient 
zodiacs  of  Egypt  and  India,  and  it  seems  probable,  therefore,  that, 
like  the  Bull  and  the  Lion,  it  was  not  representative  of  any  particular 
individual. 

73.  Capricornus     (Map  IV).      September.  —  This,   the 
eleventh  of  the  zodiacal  constellations,  follows  Sagittarius  on 
the  east.    It  has  no  bright  stars,  but  the  configuration  formed 
by  the  two  Alphas  (ax  and  a2)  with  each  other  and  with  Beta, 
3°  south,  is  characteristic,  and  not  easily  mistaken  for  any- 
thing else.     The  two  Alphas,  a  pretty  double  to  the  naked 
eye,  lie  on  the  line  drawn  from  Beta  Cygni  (at  the  foot 
of  the  cross)  through  Altair,  and  produced  about  25°. 

Some  say  that  this  constellation  represents  the  god  Pan,  who  was 
represented  by  the  Greeks  as  having  the  legs  of  a  goat  and  the  head 
of  a  man.  Others  find  in  the  goat  Amalthea  (the  foster-mother  of 
the  infant  Jupiter),  who  is  also,  it  will  be  remembered,  represented 
in  the  constellation  of  Auriga. 

74.  Delphinus,  the  Dolphin   (Map  IV).     September. — 

This  constellation,  though  small,  is  one  of  the  ancient  forty- 
eight  and  is  unmistakably  characterized  by  the  rhombus  of 
third-magnitude  stars  known  as  "  Job's  Coffin."  It  lies 
about  15°  east  of  Altair.  There  are  a  few  stars  visible 
to  the  naked  eye,  in  addition  to  the  four  that  form  the 
rhombus.  Epsilon,  about  3°  to  the  southwest,  is  the  only 
conspicuous  one. 


60  LESSONS  IN  ASTRONOMY 

Gamma,  at  the  northwest  angle  of  the  rhombus,  is  a  very  pretty 
double  star.  Beta  is  also  a  very  close  and  rapid  binary,  beyond  the 
reach  of  all  but  large  telescopes. 

This  is  the  dolphin  that  preserved  the  life  of  the  musician  Arion, 
who  was  thrown  into  the  sea  by  sailors,  but  carried  safely  to  land 
upon  the  back  of  the  compassionate  fish,  who  loved  his  music. 

75.  Equuleus,  the  Little  Horse  (Map  IV).     This  little  constella- 
tion, simply  a  horse's  head,  though  still  smaller  than  the  Dolphin 
and  less  conspicuous,  is  also  one  of  Ptolemy's.     It  lies  about  20°  due 
east  of  Altair,  and  10°  southeast  of  the  Dolphin.     (See  map.) 

76.  Lacerta,  the  Lizard  (Maps  I  and  IV).     This  is  one  of  Heve- 
lius's  modern  constellations,  lying  between  Cygnus  and  Andromeda, 
with  no  stars  above  the  4£  magnitude,  and  of  no  importance  for  our 
purposes. 

77.  Pe'gasus  (not  Pegas'us)  (Map  IV).     October.  —  This 
winged  horse  covers  an  immense  space.     Its  most  notable 
configuration  is  the  "  great  square,"  formed  by  the  second- 
magnitude    stars    Alpha    (Markab),    Beta,    and    Gamma 
Pegasi,  in  connection  with  Alpha  AndromedaB  (sometimes 
lettered  Delta  Pegasi)  at  its  northeast  corner.     The  stars 
of  the  square  lie  in  the  body  of  the  horse,  which  has  no 
hind  quarters.     A  line  drawn  from  Alpha   Andrbmedse 
through  Alpha  Pegasi,  and  produced  about  an  equal  dis- 
tance, passes  through  Xi  and  Zeta  in  the  animal's  neck 
and  reaches  Theta  in  his  ear.     Epsilon  (Enif],  the  bright 
star  8°  northwest  of  Theta,  marks  his  nose.     The  fore  legs 
are  in  the  northwestern  part  of  the  constellation  just  east 
of  Cygnus  and  are  marked,  one  of  them  by  the  stars  Eta  and 
Pi,  and  the  other  by  Iota  and  Kappa.    15  M.  Pegasi  is  a  fine 
cluster  but  little  inferior  to  that  in  Hercules. 

Pegasus  is  the  winged  horse  which  sprang  from  the  blood  of 
Medusa,  after  Perseus  had  cut  off  her  head.  He  fixed  his  residence 
on  Mt.  Helicon,  where  he  was  the  favorite  of  the  Muses,  and  after 


UUANOGRAPHY  61 

being  tamed  by  Minerva  he  was  given  to  Bellerophon  to  aid  him  in 
conquering  the  Chimsera.  After  the  destruction  of  the  monster, 
Bellerophon  attempted  to  ascend  to  heaven  upon  Pegasus,  but  the 
horse  threw  off  his  rider  and  continued  his  flight  to  the  stars. 

78.  Aquarius,  the  Water-Bearer  (Map  IV).     October. - 

This,  the  twelfth  and  last  of  the  zodiacal  constellations, 
extends  more  than  3£h  in  right  ascension,  covering  a  con- 
siderable region  which  by  rights  ought  to  belong  to  Capri- 
cornus.  The  most  notable  configuration  is  the  little  Y  of 
third-  and  fourth-magnitude  stars  which  marks  the  "  water- 
jar"  from  which  Aquarius  pours  the  stream  that  meanders 
down  to  the  southeast  and  south  for  30°,  till  it  reaches 
the  Southern  Fish.  The  middle  of  the  Y  is  about  18° 
south  and  west  of  Alpha  Pegasi  and  lies  almost  exactly 
on  the  celestial  equator. 

Zeta,  the  central  star  of  the  Y,  is  a  pretty  and  interesting  double 
star ;  distance,  about  4".  The  "  green  nebula,"  nearly  on  the  line 
from  Alpha  through  Beta,  produced  about  its  own  length,  1£°  west 
of  Nu,  is  a  planetary  nebula  and  curious  from  the  vividness  of  its 
color. 

There  are  various  opinions  respecting  the  origin  of  this  constel- 
lation. According  to  a  Greek  legend  it  represents  Deucalion,  the 
hero  of  the  Greek  Deluge;  but  among  the  Egyptians  it  evidently 
had  reference  to  the  rising  and  falling  of  the  Nile. 

79.  Piscis  Austrinus  (or  Australis),  the  Southern  Fish 
(Map    IV).     October.  —  This    small    constellation,    lying 
south  of  Capricornus  and  Aquarius   in  the  stream  that 
issues   from    the    Water-Bearer's,  urn,    presents   little    of 
interest.     It  has  one  bright  star,  Fomalhaut  (pronounced 
Fomal-hawt1),  of  the  1|  magnitude,  which  is  easily  recog- 
nized from  its  being  nearly  on  the  same  hour-circle  with 
the  western  edge  of  the  Great  Square  of  Pegasus,  45°  to 


62  LESSONS  IN  ASTRONOMY 

the  south  of  Alpha  Pegasi,  and  solitary,  having  no  star 
exceeding  the  fourth  magnitude  within  15°  or  20°.  An 
incorrect  pronunciation  (Fomalo)  is  common;  but  "haut" 
is  Arabic,  not  French. 

This  constellation  is  by  some  said  to  represent  the  transformation 
of  Venus  into  a  fish,  when  fleeing  from  Typhon  (but  see  Pisces). 

South  of  the  Southern  Fish,  barely  rising  above  the  southern  hori- 
zon, lie  the  constellations  of  Microscopium  and  Grus.  The  former  is 
of  no  account.  In  the  southern  hemisphere  Grus  is  a  conspicuous 
constellation,  and  its  two  brightest  stars,  Alpha  and  Beta,  of  the 
second  magnitude,  rise  high  enough  to  be  seen  in  latitudes  south 
of  Washington.  They  lie  about  20°  south  and  west  of  Fomalhaut. 


URANOGRAPHY 


63 


CHAPTER   III 

LATITUDE,  TIME,  AND  LONGITUDE 

Latitude,  and  the  Aspect  of  the  Celestial  Sphere  —  Time  —  Longitude  —  The 
Place  of  a  Heavenly  Body 

80,  Latitude  defined.  —  In  Geography  the  latitude  of  a 
place  is  "usually  denned  simply  as  its  distance  north  or 
south  of  the  equator,  measured  in  degrees.  This  is  not 
explicit  enough,  unless  it  is  stated  how  the  degrees  them- 
selves are  to  be  measured.  There  would  be  no  difficulty 
if  the  earth  were  a  perfect  sphere ;  but  since  the  earth 
is  a  little  flattened  at  the  poles,  the  degrees  (geographical) 
are  of  somewhat  different  lengths  at  different  parts  of 
the  earth.  The  exact  definition  of  the  astronomical  lati- 
tude of  a  place  istJie  angle  between  the  direction  of  Jjie 
observer's  plumb-line  and  the  plane  of  the  earth's  equators- 

-L  _         -L       _  *  J.  .  * 

ancT  this  is  the  same  as  the  altitude,  or  angle  of  elevation, 
of  the  pole,  as  will  be  clear  from  Fig.  7.  Here  the  angle 
ONQ  is  the  latitude  as  denned.  If  now  at  0  we  draw 
HH1  perpendicular  to  OZ,  it  will  be  a  level  line,  and  will 
point  to  the  horizon.  From  0  also  draw  OP",  parallel  to 
CP\  the  earth's  axis.  Since  OP"  and  CP'  are  parallel, 
they  will  be  directed  apparently  to  the  same  point  in  the 
celestial  sphere  (Sec.  6),  and  this  point  is  the  celestial 
pole.  The  angle  H' OP"  is  therefore  the  altitude  of  the 
pole,  as  seen  at  0,  and  it  obviously  equals  ONQ ;  and  this 
is  true  whether  the  earth  be  a  sphere,  or  whatever  its 

64 


LATITUDE 


65 


form.  This  fundamental  relation,  that  the  Altitude  <>f  the 
Pole  is  Identical  with  the  Observer's  Latitude,  cannot  be 
too  strongly  impressed  on  the  mind. 

81.  Method  of  measuring  the  Latitude.  —  The  most  obvi- 
ous method  is  to  observe,  with  a  suitable  instrument,  the 
altitude  of  some  star  near  the  pole  (a  "  circumpolar  "  star) 
at   the   moment  when 

it  is  crossing  the  me-  Z 

ridian  above  the  pole, 
and  again  twelve  hours 
later,  when  it  is  once 
more  on  the  meridian 
below  the  pole.  In  the 
first  position  its  eleva- 
tion is  the  greatest  pos- 
sible ;  in  the  second, 
the  least.  The  average 

Of  these   two  altitudes,  Fl«.  7. -Relation  of  Latitude  to  the  Elevation 

of  the  Pole 

when  corrected  for  re- 
fraction, is  the  latitude  of  the  observer.     It  is  exceedingly 
important  that  the  student  understand  this  simple  method 
of  determining  the  latitude. 

The  instrument  ordinarily  used  for  making  observations  of  this 
kind  at  an  observatory  is  called  a  meridian  circle,  and  a  brief  descrip- 
tion is  given  in  the  Appendix.  (See  Sec.  418.) 

82.  Refraction When  we  observe  the  altitude  of  a 

heavenly  body  with  any  instrument  we  do  not  find  it  the 
same  that  it  would  be  if  our  atmosphere  had  no  effect 
upon  the  rays  of  light.     As  they  enter  the  earth's  atmos- 
phere they  are  bent  downward  by  "  refraction,"  excepting 
only  such  as    come   from   exactly    overhead.     Since  the 


66  LESSONS  IN  ASTRONOMY 

observer  sees  the  object  in  the  direction  in  which  the  rays 
enter  the  eye,  without  any  reference  to  its  real  position,  this 
bending  down  of  the  rays  causes  every  object  seen  through 
the  air  to  look  higher  up  in  the  sky  than  it  would  be  if  the 
air  were  absent ;  and  we  must  therefore  correct  the  observed 
altitude  by  subtracting  the  proper  amount.  Under  ordinary 
conditions,  refraction  elevates  a  body  at  the  horizon  about 
35',  so  that  the  sun  and  moon  in  rising  appear  clear  of  the 
horizon  while  they  are  still  wholly  below  it.  The  refraction 
correction  diminishes  very  rapidly  as  the  body  rises.  At 
an  altitude  of  only  5°  the  refraction  is  but  10';  at  44°, 
it  is  about  V ;  and  at  the  zenith,  zero,  of  course. 

Its  amount  at  any  given  time  is  affected  quite  sensibly,  however, 
by  the  temperature  and  by  the  height  of  the  barometer,  increasing 
as  the  thermometer  falls  or  as  the  barometer  rises  ;  so  that  whenever 
great  accuracy  is  required  in  measures  of  altitude  we  must  have 
observations  of  both  the  barometer  and  thermometer  to  go  with  the 
reading  of  the  circle.  There  are  tables  by  which  the  refraction  can 
be  computed  for  an  object  at  any  altitude  and  in  any  state  of  the 
weather.  But  this  indispensable  correction  is  very  troublesome,  and 
always  involves  more  or  less  error. 

(For  other  methods  of  determining  the  latitude,  see 
Appendix,  Sec.  424.) 

83,  Effect  of  the  Observer's  Latitude  upon  the  Aspect  of 
the  Heavens ;  the  Right  Sphere.  —  If  the  observer  is  situ- 
ated at  the  earth's  equator,  —  i.e.,  in  latitude  zero,  —  the 
celestial  poles  will  evidently  be  on  the  horizon,  and  the 
celestial  equator  will  pass  through  the  zenith  and  coincide 
with  the  prime  vertical  (Sec.  11).  At  the  earth's  equator, 
therefore,  all  heavenly  bodies  will  rise  and  set  vertically, 
and  their  diurnal  circles  will  be  equally  divided  by  the 


ASPECT  OF  THE  HEAVENS 


67 


horizon,  so  that  they  will  be  twelve  hours  above  it  and 
twelve  hours  below  it,  and  the  length  of  the  night  (neglect- 
ing refraction)  will  always  equal  that  of  the  day.  This 
aspect  of  the  heavens  is  called  the  right  sphere. 

84.  Parallel  Sphere.  —  If  the  observer  is  at  one  of  the 
poles  of  the  earth,  where  the  latitude  equals  90°,  then  the 
corresponding  celestial  pole  will  be  exactly  overhead,  and 
the  celestial  equator  will  coincide  with  the  horizon.  If  he 
is  at  the  north  pole,  all 
the  stars  north  of  the 
celestial  equator  will  re- 
main permanently  visible, 
never  rising  or  setting, 
but  sailing  around  the  sky 
on  parallels  of  altitude, 
while  the  stars  south  of 
the  equator  will  never  rise 
to  view.  Since  the  sun 
and  the  moon  move  in 
such  a  way  that  during 
half  the  time  they  are 
north  of  the  equator  and 


FIG.  8.— The  Oblique  Sphere 


half  the  time  south  of  it,  they  will  therefore  be  half  the 
time  above  the  horizon  and  half  the  time  below  it  (that  is, 
approximately,  since  refraction  has  a  noticeable  effect). 
The  moon  will  be  visible  for  about  a  fortnight  at  a  time, 
and  the  sun  for  about  six  months. 

85.    The  Oblique  Sphere At  any  station  between  the 

pole  and  the  equator  the  pole  will  be  elevated  above  the 
horizon,  and  the  stars  will  rise  and  set  in  oblique  circles, 
as  shown  in  Fig.  8.  Those  stars  whose  distance  from  the 


68  LESSONS  IN  ASTRONOMY 

elevated  pole  is  less  than  PN,  the  latitude  of  the  observer, 
will  never  set,  the  radius  of  this  circle  of  perpetual  appa- 
rition being  just  equal  to  the  altitude  of  the  pole,  and 
becoming  larger  as  the  latitude  increases.  On  the  other 
hand,  stars  within  the  same  distance  of  the  depressed  pole 
will  lie  within  the  circle  of  perpetual  occultation,  and  will 
never  rise  above  the  observer's  horizon.  An  object  which 
is  exactly  on  the  celestial  equator  will  have  its  diurnal 
circle,  EQ  WQ!,  equally  divided  by  the  horizon,  and  will  be 
above  the  horizon  just  as  long  as  below  it. 

For  an  observer  in  the  United  States  a  star  north  of  the 
equator  will  have  more  than  half  of  its  diurnal  circle  above 
the  horizon,  and  will  be  visible  for  more  than  twelve  hours 
of  each  day;  as,  for  instance,  the  star  at  A.  Whenever 
the  sun  is  north  of  the  celestial  equator  the  day  will  there- 
fore be  longer  than  the  night  for  all  stations  in  northern 
latitude  ;  how  much  longer  will  depend  both  on  the  latitude 
of  the  place  and  the  sun's  distance  from  the  equator  (the 
sun's  declination}. 

86.  Moreover,  when  the  sun  is  north  of  the  equator,  it 
will,  in  the  northern  latitudes,  rise  at  a  point  north  of  east, 
as  at  B  in  the  figure,  and  will  continue  to  shine,  on  the 
north  side  of  every  wall  that  runs  east  and  west  until,  as 
it  ascends,  it  crosses  the  prime  vertical,  EZW,  at  some 
point,  as  V.  In  the  latitude  of  New  York  the  sun  in  June 
is  south  of  the  prime  vertical  for  only  about  eight  hours 
of  the  whole  fifteen  during  which  it  is  above  the  horizon. 
During  seven  hours  of  the  day,  therefore,  it  shines  into 
north  windows. 

If  the  latitude  of  the  observer  is  such  that  PN,  in  the 
figure,  is  greater  than  the  sun's  polar  distance  at  the  time 


TIME  69 

when  it  is  farthest  north,  the  sun  at  midsummer  will  make 
a  complete  circuit  of  the  heavens  without  setting,  thus 
producing  the  phenomenon  of  the  "  midnight  sun,"  visible 
at  the  North  Cape  and  at  all  stations  within  the  Arctic 
Circle. 

87.  A  celestial  globe  will  be  of  great  use  in  studying 
these  diurnal  phenomena.     The  north  pole  of  the  globe 
must  be  elevated  to  an  angle  equal  to  the  latitude  of  the 
observer,  which  can  be  done  by  means  of  the  degrees  marked 
on  the  metal  meridian  ring.     It  will  then  be  seen  at  once 
what  stars  never  set,  which  ones  never  rise,  and  during 
what  part  of  the  twenty-four  hours  any  heavenly  body  at 
a  known  distance  from  the  equator  is  above  or  below  the 
horizon.     (For  description  of  the  celestial  globe,  see  Appen- 
dix, Sec.  400.) 

TIME 

Time  is  usually  denned  as  "  measured  duration,"  and 
the  standard  unit  of  time  has  always  been  obtained  in  some 
way  from  the  length  of  the  day. 

88.  Apparent  Solar  Time.  —  The  most  natural  way,  since 
we  are  obliged  to  regulate  our  lives  by  the  sun,  is  to  reckon 
time  by  him ;  i.e.,  to  call  it  noon  when  the  sun  is  on  the 
meridian  and  highest,  and  to  divide  the  day  from  one  noon 
to  another  into  its  hours,  minutes,  and  seconds.     Time 
thus  reckoned  is  called  apparent  solar  time  (see  Appendix, 
Sec.  422),  and  is  the  time  shown  by  a  correctly  adjusted 
sundial.     But  because  the  sun's  eastward  motion  in  the 
sky  is  not  uniform  (owing  to  the  oval  form  of  the  earth's 
orbit  and  its  inclination  to  the  equator),  these  apparent 
solar  days  are  not  exactly  of  the  same  length.     Thus,  for 


70  LESSOXS  IN  ASTRONOMY 

instance,  the  interval  from  noon  of  December  22  to  noon 
of  December  23  is.  nearly  a  minute  longer  than  the  inter- 
val between  the  noons  of  September  15  and  16.  As  a  con- 
sequence, it  is  only  by  very  complicated  and  expensive 
machinery  that  a  watch  or  clock  can  be  made  to  keep  time 
precisely  with  the  sundial;  nor  is  it  worth  while,  since 
it  is  much  better  to  have  the  timekeeper  uniform  in  its 
motion.  Apparent  solar  time  is  now  used  only  in  commu- 
nities where  clocks  and  watches  are  rare  and  sundials  are 
the  usual  timepieces,  as  in  China  and  in  much  of  the  "East. 

89.  Mean  Solar  Time.  —  At  present,  for  civil  ancf  busi- 
ness purposes,  time  is  almost  universally  reckoned  Jn  days 
ail~i)f~  which  have  precisely  the  same  length,  and  are  just 
equal  to  the  average  apparent  solar  day;  and 

called  mean  solar  time  (Appendix,  Sec.  422),  is  that  whic 
is  kept  by  all  good  timepieces. 

Sundial  time  agrees  with  mean  time  four  times  a  year;  viz.,  upon 
April  15,  June  14,  September  1,  and  December  24.  The  greatest 
differences  occur  on  November  2  and  February  11,  when  the  sundial 
is  respectively  16m208  fast  of  the  clock  and  14m30s  slow.  .  During 
the  summer  the  difference  never  exceeds  6m.  Tills,  variable  differ- 
ence  is  called  the  Equation  of  Time,  and  is  given  i 
every  day  in  the  year. 

90.  The  Civil  Day  and  the  Astronomical  Day.  —  The  astronomical 
day  begins  at  noon  ;  the  civil  day  at  midnight,  twrelve  hours  earlier. 
Astronomical   mean  time  is  reckoned    around  through  the  whole 
twenty  -four  hours,  instead  01  oeing  counted  in  two  series  o 


hours  each.  Thus,  8  A.M.  of  Tuesday,  August  12,  civil  reckoning, 
is  Monday,  August  11,  20h,  of  astronomical  reckoning.  Beginners 
need  to  bear  this  in  mind  in  referring  to  the  almanac. 

91.  Jidereal  Time,  or  Time  reckoned  by  the  Stars.  —  As 
has  been  said  (Sec.  17),  the  sun  is  not  fixed  on  the  celestial 


DETERMINATION   OF  TIME  71 

sphere,  but  appears  to  creep  completely  around  it  once 
a  year,  moving  :daily  about  one  degree  eastward  among  the 
stars.  The~interval  from  noon  to  noon  does  not  therefore 
correspond  to  the  true  diurnal  revolution  of  the  heavens. 
If  we  reckoned  by  the  interval  between  two  successive 
passages  of  any  given  star  across  the  observer's  meridian, 
we  should  find  that  this  true  day,  the  sidereal  day,  as  it 
is  (-idled,  is  nearly  4m  shorter  (3m56s.9)  than  the  ordinary 
solar  day,  from  noon  to  noon,  the  relation  being  such  that 
in  a  year  the  number  of  sidereal  days  exceeds  that  of  solar  by 
exactly  one.  For  many  purposes,  astronomers  find  it  much 
more  convenient  to  reckon  by  the  stars  than  by  the  sun. 
They  count  the  time,  however,  not  by  any  real  star,  but 
from  the  Vernal  Equinox,  the  sidereal  clock  being  so  set 
and  regulated  that  it  always  shows  zero  hours,  minutes, 
and  seconds  (sidereal  noon)  at  the  moment  when  the  vernal 
equinox  is  on  the  meridian.  (See  Appendix,  Sec.  422.) 

This  kind  of  time,  of  course,  would  not  answer  for  busi- 
ness purposes,  since  its  noon  comes  at  all  hours  of  the  day 
and  night  at  different  seasons  of  the  year.  The  almanac 
gives  data  by  which  sidereal  time  and  mean  solar  time  can 
be  easily  converted  into  each  other. 

92,  The  Determination  of  Time. — In  practice,  the 
problem  always  takes  the  shape  of  finding  the  error  of  a 
timepiece  of  some  sort ;  i.e.,  ascertaining  how  many  seconds 
it  -is  fast  or  slow.  The  instrument  now  ordinarily  used 
for  the  purpose  is  the  transit  instrument,  which  is  a  small 
telescope  mounted  on  an  axis,  placed  exactly  east  and 
west,  and  level,  so  that  as  the  telescope  is  turned  it  will 
follow  the  meridian ;  at  least,  the  middle  cross-wire  in  the 
field  of  view  will  do  so.  It  is  the  same  as  the  meridian 


72  LESSONS  IN  ASTRONOMY 

circle,  except  that  it  does  not  require  the  costly  graduated 
circle  with  its  appendages.  (For  description,  see  Appendix, 
Sec.  416.) 

To  determine  with  the  transit  the  error  of  the  sidereal 
clock  which  is  ordinarily  used  in  connection  with  it,  it  is 
only  necessary  to  observe  the  exact  time  indicated  by  the 
clock  when  some  star  whose  right  ascension  is  known 
passes,  or  "  transits,"  the  middle  wire  of  the  instrument. 

93.  The  right  ascension  of  a  star  (Sec.  18)  is  the  num- 
ber of  "  hours  "  of  arc  (measured  along  the  equator)  by  which 
the  star  is  east  of  the  vernal  equinox ;  and  therefore  when  the 
star  is  on  the  meridian  the  right  ascension  also  equals  the 
number  of  hours,  minutes,  and  seconds  since  the  transit 
of  the  vernal  equinox.  In  other  words,  we  may  say  that"- 
the  right  ascension  of  a  star  is  the  local  sidereal  time  at  the 
moment  of  its  meridian  transit.  (This  is  often  called  the 
observatory  definition  of  right  ascension.)  For  instance, 
the  right  ascension  of  Vega  (Alpha  Lyrse)  is  18h33m.  If 
we  observe  its  transit  to  occur  at  18h40m  by  the  clock,  the 
clock  is  obviously  7m  fast. 

With  a  good  instrument,  a  skilled  observer  by  observing 
a  number  of  stars  can  thus  determine  the  clock-error 
within  about  one-thirtieth  of  a  second  of  time. 

To  get  solar  time,  we  may  observe  the  sun  itself,  the 
moment  of  its  transit  being  "  apparent  noon."  But  it  is 
better,  and  it  is  usual,  to  get  the  sidereal  time  first,  and  to 
deduce  from  that  the  solar  time  by  means  of  the  necessary 
data  which  are  furnished  in  the  almanac. 

The  method  by  the  transit  instrument  is  most  used,  and  is,  on  the 
whole,  the  most  convenient ;  but  since  the  instrument  requires  to  be 
mounted  upon  a  firm  pier,  it  is  not  always  available.  When  not,  we 


LONGITUDE  73 

use  some  one  of  various  other  methods,  for  which  reference  must  be 
made  to  the  General  Astronomy.  At  sea,  and  by  travelers  on  scientific 
expeditions,  the  time  is  usually  determined  by  observing  the  altitude 
of  the  sun  with  a  sextant  some  hours  before  or  after  noon.  (See 
Appendix,  Sec.  427.) 

LONGITUDE 

94.  The  problem  of  finding  the  longitude  is  in  many 
respects  the  most  important  of  what  may  be  called  the 
"  economic "  problems  of  Astronomy;  i.e.,  those  of  business 
utility  to  mankind.  The  great  observatories  of  Greenwich 
and  Paris  were  founded  for  the  express  purpose  of  fur- 
nishing the  necessary  data  to  enable  the  sailor  to  determine 
his  longitude  at  sea;  and  the  English  government  has 
given  great  prizes  for  the  construction  of  clocks  and  chro- 
nometers fit  to  be  used  in  such  determinations. 

The  longitude  of  a  place  on  the  earth  is  defined  as  the 
arc  of  the  equator  intercepted  between  the  meridian  which 
passes  through  the  place  and  some  meridian  which  is  taken 
as  the  standard.1 

Now,  since  the  earth  turns  on  its  axis  at  a  uniform  rate, 
this  arc  is  strictly  proportional  to,  and  may  be  measured  by, 
the  interval  of  sidereal  time  between  the  transits  of  a  given 
star  across  the  two  meridians,  or  by  the  interval  of  mean 
solar  time  between  the  transits  of  the  sun.  The  longitude 
of  a  place  may  therefore  be  defined  as  the  amounT~try--w&ich 
the  time  at  G-reenwich  is  earlier  or  later  than,  the  time  at  the 
station  of  the  observer,  and  this  whether  we  reckon  by  solar 
or  by  sidereal  time.  Accordingly,  terrestrial  longitude  is 

1  As  to  the  standard  meridian,  there  is  a  variation  of  usage  among  dif- 
ferent nations.  The  French  reckon  from  the  meridian  of  Paris,  but  most 
other  nations  use  the  meridian  of  Greenwich,  at  least  at  sea. 


74  LESSONS  IN  ASTRONOMY 

usually  reckoned  in  hours,  minutes,  and  seconds,  rather 
than  hi  degrees.  Since  the  observer  can  easily  find  his 
own  local  time  by  the  transit  instrument,  or  by  some  of 
the  many  other  methods,  the  knot  of  the  problem  is  simply 
this :  to  find  the  Greenwich  time  at  any  moment  without 
going  to  Greenwich;  then  we  get  the  longitude  at  once 
by  simply  comparing  it  with  our  own  time. 

95.  Methods  of  determining  Longitude. — Incomparably 
the  best  method,  whenever  it  is  available,  is  to  make  a 
direct  telegraphic  comparison  between  the  clock  of   the 
observer  and  that  of  some  station  the  longitude  of  which 
is  known.     The  difference  between  the  two  clocks,  duly 
corrected  for  their  "  errors  "  (Sec.  92),  will  be  the  true  dif- 
ference of  longitude.    The  wireless  telegraph  is  now  being 
used  for  this  purpose,  and  is  especially  convenient  at  sea, 
where   ordinary  telegraphic   communication  is  impossible. 
Time  signals  are  sent  out  daily  from  Arlington,  Va.,  and 
any  one  within  the  radius  of  these  signals  can  get  accurate 
eastern  standard  time,  which  is  exactly  five  hours  behind 
Greenwich  time. 

96,  A  second  method  is  to  use  a  chronometer,  which  is 
simply  a  very  accurate  watch.     This  is  set  to  Greenwich 
time  at  some  place  whose  longitude  is  known,  and  after- 
wards is  supposed  to  keep  that  time   wherever  carried. 
The  observer  has  only  to  compare  his  own  local  time, 
determined  with  the  transit  instrument  or  sextant,  with 
the  time  shown  by  such  a  chronometer,  and  the  difference 
is  his  longitude  from  Greenwich.     This  is  the    ordinary 
method  at  sea. 

Practically,  of  course,  no  chronometer  goes  absolutely  without 
gaining  or  losing  ;    hence,  it  is  always  necessary  to  know  and  to 


LOCAL  AND  STANDARD  TIME         75 

allow  for  its  gain  or  loss  since  the  time  it  was  last  set.  Moreover,  it 
is  never  safe  to  trust  a  single  chronometer,  because  of  the  liability  of 
such  instruments  to  change  their  rate  in  transportation.  A  number 
(three  or  more)  should  be  used,  if  possible. 

Before  the  days  of  telegraphs  and  chronometers,  astrono- 
mers were  generally  obliged  to  get  their  Greenwich  time 
from  the  moon,  which  may  be  regarded  as  a  clock-hand 
with  the  stars  for  dial  figures;  but  observations  of  this 
kind  are  troublesome,  and  the  results  inaccurate  as  com- 
pared with  those  obtained  by  the  telegraph  and  chronom- 
eter. (For  further  details,  see  General  Astronomy, 
Arts.  109-116.) 

97.  Local  and  Standard  Time.  —  Until  recently  it  has 
been  always  customary  to  use  local  time,  each  station 
determining  its  own  time  by  its  own  observations,  and 
having,  therefore,  a  time  differing  from  that  of  all  other 
stations  not  on  the  same  meridian.  Before  the  days  of 
the  telegraph,  and  while  traveling  was  comparatively 
slow,  this  was  best.  At  present  there  are  many  reasons 
why  it  is  better  to  give  up  the  old  system  in  favor  of  a 
system  of  standard  time.  The  change  greatly  facilitates 
all  railway  and  telegraphic  business,  and  makes  it  practi- 
cally easy  for  everybody  to  have  accurate  time,  since  the 
standard  time  can  be  daily  wired  from  some  headquarters 
to  every  telegraph  office. 

According  to  the  system  now  established  in  North 
America,  there  are  five  such  standard  times  in  use,  —  the 
colonial,  the  eastern,  the  central,  the  mountain,  and  the 
Pacific,  —  which  differ  from  Greenwich  time  by  exactly 
four,  five,  six,  seven,  and  eight  hours  respectively,  the 
minutes  and  seconds  being  everywhere  identical,  and  the 


76  LESSONS  IN  ASTRONOMY 

same  with  those  of  the  clock  at  Greenwich.  In  order  to 
determine  the  standard  time  by  observation,  it  is  neces- 
sary only  to  find  the  local  time  by  one  of  the  methods 
given  and  correct  it  according  to  the  observer's  longitude 
from  Greenwich. 

98.  Where  the  Day  begins.  —  It  is  clear  that  if  a  trav- 
eler were  to  start  from  Greenwich  on  Monday  noon,  and 
travel  westward  as  fast  as  the  earth  turns  to  the  east 
beneath  his  feet,  he  would  have  the  sun  upon  the  meridian 
all  day  long,  and  it  would  be  continual  noon.  But  what 
noon?  It  was  Monday  when  he  started,  and  when  he 
gets  back  to  London  twenty-four  hours  later  it  will  be 
Tuesday  noon  there,  and  yet  he  has  had  no  intervening 
night.  When  did  Monday  noon  become  Tuesday  noon? 

It  is  agreed  among  mariners  to  make  the  change  of 
date  at  the  180£h  meridian  from  Greenwich.  Ships  cross- 
ing this  line  from  the  east  skip  one  day  in  so  doing.  If 
it  is  Monday  afternoon  when  a  ship  reaches  the  line,  it 
becomes  Tuesday  afternoon  the  moment  she  passes  it,  the 
intervening  twenty-four  hours  being  dropped  from  the 
reckoning  on  the  log-book.  Vice  versa,  when  a  vessel 
crosses  the  line  from  the  western  side  it  counts  the  same 
day  twice,  passing  from  Tuesday  back  to  Monday. 

This  180th  meridian  passes  mainly  over  the  ocean,  hardly  touch- 
ing land  anywhere.  There  is  some  irregularity  as  to  the  date  actually 
used  on  the  different  islands  of  the  Pacific.  Those  which  received 
their  earliest  European  inhabitants  via  the  Cape  of  Good  Hope  have, 
for  the  most  part,  adopted  the  Asiatic  date,  even  if  they  really  lie 
east  of  the  180th  meridian,  while  those  which  were  first  approached 
via  Cape  Horn  have  the  American  date.  When  Alaska  was  trans- 
ferred from  Russia  to  the  United  States  it  was  necessary  to  drop 
one  day  of  the  week  from  the  official  dates. 


PLACE  OF  A  CELESTIAL  OBJECT  77 

DETERMINATION   OF   THE   POSITION  OF   A 
HEAVENLY  BODY 

As  the  basis  of  our  investigations  in  regard  to  the 
motions  of  the  heavenly  bodies,  we  require  a  knowledge 
of  their  places  in  the  sky  at  known  times.  By  determin- 
ing the  "  place "  of  a  body,  we  mean  finding  its  right 
ascension  and  declination. 

99.  By  the  Meridian  Circle  (see  Appendix,  Sec.  418). — 
If  a  body  is  bright  enough  to  be  seen  by  the  telescope  of  the 
meridian  circle,  and  comes  to  the  meridian  in  the  nighttime, 
its  right  ascension  and  declination  are  best  determined  by 
the  Meridian  Circle.      If  the  instrument  is  in  exact  adjust- 
ment, the  right  ascension  of  the  body  is  simply  the  sidereal 
time  when  it  crosses  the  middle  vertical  wire  of  the  reticle. 
The   "  circle-reading,"  on  the   other  hand,   corrected  for 
refraction,  gives  the  declination.     A  single  complete  obser- 
vation with  the  meridian  circle  determines  accurately  both 
the  right  ascension  and  the  declination  of  the  object. 

100.  By  the  Equatorial.  —  If  the  body  —  a  comet,  for 
instance  —  is  too  faint  to  be  observed  by  the  telescope  of 
the  meridian  circle,  seldom  very  powerful,  or  comes  to  the 
meridian  only  in  the  daytime,  we  usually  accomplish  our 
object  by  using  the  equatorial  (Appendix,  Sec.  414),  and 
determine   the  position  of   the  body  by  measuring  with 
some  kind  of  "  micrometer  "  the  difference  of  right  ascen- 
sion and  declination  between  it  and  a  neighboring  star 
whose  place  is  given  in  some  star-catalogue. 


CHAPTER   IV 

THE  EARTH 

Its  Form  and  Dimensions;   its  Rotation,   Mass,   and  Density;   its  Orbital 
Motion  and  the  Seasons  —  Precession  —  The  Year  and  the  Calendar 

101.  In    a   science   which    deals    with   the    "heavenly 
bodies,"  there  might  seem  at  first  to  be  no  place  for  the 
Earth.     But  certain  facts  relating  to  the  Earth,  just  such 
as  we  have  to  investigate  with  respect  to  her  sister  planets, 
are  ascertained  by  astronomical  methods,  and  a  knowledge 
of  them  is  essential  as  a  base  of  operations.    In  fact,  Astron- 
omy, like  charity,  "  begins  at  home,"  and  it  is  impossible  to 
go  far  in  the  study  of  the  bodies  which  are  strictly  "  heav- 
enly "  until  we  have  first  acquired  some  accurate  knowledge 
of  the  dimensions  and  motions  of  the  earth  itself. 

102.  The  astronomical  facts  relating  to  the  earth  are 
broadly  these : 

1.  The  earth  is  a  great  ball  about  7920  miles  in  diameter. 

2.  It  rotates  on  its  axis  once  in  twenty-four  "  sidereal " 
hours. 

3.  It  is  not  exactly  spherical,  but  is  slightly  flattened  at 
the  poles ;  the  polar  diameter  being  nearly  twenty-seven 
miles,  or  about  ^^  part  less  than  the  equatorial. 

4.  It  has  a  mean  density  of  about  5.5   times  that  of 
water,  and  a  mass  represented  in  tons  by  6  with  twenty- 
one  ciphers  following  (six  thousand  millions  of  millions 
millions  of  tons). 

78 


THE  EARTH  79 

5.  It  is  flying  through  space  in  its  orbital  motion  around 
the  sun,  with  a  velocity  of  about  eighteen  and  a  half  miles 
a  second;  i.e.,  about  seventy-five  times  as  swiftly  as  an 
ordinary  cannon-ball. 

103.  The  Earth's  Approximate  Form  and  Size It  is 

not  necessary  to  dwell  on  the  jmlinary  proofs  of  the  globu- 
larity  of  the  earth.     We  simply  mention  them. 

1.  It  can  be  sailed  around. 

2.  The  appearance  of  vessels  coming  in  from  the  sea 
indicates  that  the  surface  is  everywhere  convex. 

3.  The  fact  that  as  one  goes  from  the  equator  towards 
the  north  the  elevation  of  the  pole  increases  in  proportion 
to  the  distance  from  the  equator,  proves  the  same  thing. 

^•L__The  outline  of  the  earth's  shadow,  as  seen  upon  the  moon 
during  lunar  eclipses,  is  such  as  only  a  sphere  could  cast. 

We  may  add,  as  to  the  smoothness  and  roundness  of  the 
earth,  that  if  the  earth  be  represented  by  an  eighteen-inch 
globe,  the  difference  between  its  greatest  and  least  diam- 
eters would  be  only  about  one-sixteenth  of  an  inch;  the 
highest  mountains  would  project  only  about  one-eightieth 
of  an  inch,  and  the  average  elevation  of  continents  and 
depths  of  the  ocean  would  be  hardly  greater  than  a  film 
of  varnish.  Relatively,  the  earth  is  really  much  smoother 
and  rounder  than  most  of  the  balls  in  a  bowling-alley. 

104.  One  of  the  simplest  methods  of  showing  the  curvature  of 
the  earth  is  the  following : 

In  an  expanse  of  still,  shallow  water  (a  long  reach  of  canal,  for 
instance)  set  a  row  of  three  poles  about  a  mile  apart,  with  their 
tops  projecting  to  exactly  the  same  height  above  the  surface.  On 
sighting  across,  it  will  then  be  found  that  the  middle  pole  projects 
above  the  line  that  joins  the  tops  of  the  two  end  ones,  and  from  the 
amount  of  this  projection,  after  due  correction  for  refraction  (which 


80 


LESSONS  IN  ASTRONOMY 


reduces  it  from  about  eight  inches  to  six  under  ordinary  conditions 
of  temperature),  a  rough  estimate  of  the  size  of  the  earth  can  be 
made.  (See  General  Astronomy,  Art.  134.) 

105.  Measure  of  the  Earth's  Diameter.  —  The  only  accu- 
rate method  of  measuring  the  diameter  of  the  earth  is  the 
following,  the  principle  of  which  is  very  simple,  and  should 

be  thoroughly  mastered  by  the 
student  : 

It  consists  infmding_the 
length  in  miles  of  an  arc  of 
the  earth's  surface  containing  a 
known  number  of  degrees.  From 
this  we  get  the  length  of  one 
degree,  and  this  gives  the  circum- 
ference of  the  earth  (since  it 
contains  360°),  and  from  this  the 
diameter  is  obtained  by  dividing 
it  by  3.14159. 

To  do  this,  we  select  two 
stations,  a  and  b  (Fig.  9),  some 
hundreds  of  miles  apart  on  the 
same  meridian,  and  determine 

the  latitude    /Qr  the  altitude   of 


FIG.  O.-Measuring  the  Earth's 
Diameter 


the  pole)  at  each  station  by 
astronomical  observation.  The  difference  of  latitude  (i.e., 
ECl  —  EC  a)  is  evidently  the  number  of  degrees  in  the  arc 
ab,  and  the  determination  of  this  difference  of  latitude 
is  the  only  astronomical  operation  necessary. 

Next,  the  distance  in  miles  between  the  two  stations 
must  be  measured.  This  is  geodetic  work,  and  it  is 
enough  for  our  purpose  here  to  say  that  it  can  be 


THE  EARTH'S  ROTATION  81 

done  with  great  precision  by  a  process  which  is  called 
"  triangulation." 

This  measurement  of  arcs  has  been  made  on  many  parts 
of  the  earth's  surface,  and  the  result  is  that  the  average 
length  of  a  degree  is  found  to  be  a  little  more  than  sixty- 
nine  miles,  and  the  mean  diameter  of  the  earth  about 
7918  miles.  The  reason  why  we  say  average  length  and 
mean  diameter  is  that  the  earth,  as  has  been  said,  is  not 
quite  spherical,  but  is  slightly  flattened  at  its  poles,  so 
that  the  lengths  of  the  degrees  differ  in  different  parts  of 
the  earth,  as  we  shall  soon  see  (Sec.  110). 

106.  The  Rotation  of  the  Earth. — Ptolemy  understood 
that  the  earth  was  round^  but  he  and  all  his  successors 
deliberately  rejected  the  theory  of  its  rotation.  Though 
the  idea  that  the  earth  might  turn  upon  an  axis  was  not 
unfamiliar,  they  considered  that  there  were  conclusive 
reasons  against  it.  At  the  time  when  Copernicus  of  Thorn, 
in  Poland  (1473-1543),  proposed  his  theory  of  the  solar 
system,  the  only  argument  he  could  urge  in  favor  of  the 
earth's  rotation l  was  that  this  hypothesis  was  much  more 
probable  than  the  older  one  that  the  heavens  themselves 
revolve.  All  the  phenomena  then  known  would  be  sen- 
sibly the  same  on  either  supposition.  The  apparent  daily 
motion  of  the  heavenly  bodies  can  be  perfectly  accounted 
for  (within  the  limits  of  such  observations  as  were  then 
possible)  either  by  supposing  that  they  are  actually  attached 
to  the  celestial  sphere,  which  turns  daily,  or  that  the  earth 

1  The  word  **  rotation  "  denotes  a  spinning  motion,  like  that  of  a  wheel 
on  its  axis.  The  word  "revolve"  is  more  general,  and  may  be  used  to 
describe  such  a  spinning  motion  or  (and  this  is  the  more  common  use  in 
Astronomy)  to  describe  the  motion  of  a  body  traveling  around  another, 
as  when  we  say  the  earth  "  revolves  "  around  the  sun. 


82 


LESSONS  IN  ASTRONOMY 


itself  spins  upon  an  axis  once  in  twenty-four  hours ;  and 
for  a  long  time  the  latter  hypothesis  did  not  seem  to  most 
people  so  reasonable  as  the  older  and  more  obvious  one. 
A  little  later,  after  the  telescope  had  been  invented,  analogy 
could  be  appealed  to ;  for  we  can  see  with  the  telescope 
that  the  sun  and  moon -and  many  of  the  planets  really 
rotate  upon  axes.  At  present  we  can  go  still  further,  and 

can  absolutely  demon- 
strate the  earth's  rota- 
tion by  experiments, 
some  of  which  even 
make  it  visible. 

107.  Foucault's  Pen- 
dulum Experiment.  - 
Among  these  experi- 
mental proofs  the  most 
impressive  is  the  "pen- 
dulum experiment" 
devised  by  Foucault  in 
1851.  From  the  dome 
of  the  Pantheon,  in 
Paris,  he  hung  a  heavy 
iron  ball  by  a  slender 
wire  more  than  200  feet 
long  (Fig.  10).  A  circular  rail,  with  a  little  ridge  of  sand 
built  upon  it,  was  placed  in  such  a  way  that  a  pin  attached 
to  the  swinging  ball  would  just  scrape  the  sand  and  leave 
a  mark  at  each  vibration.  To  put  the  ball  in  motion,  it  was 
drawn  aside  by  a  cotton  cord  and  left  for  some  hours,  until 
it  came  absolutely  to  rest.  Then  the  cord  was  burned  off, 
and  the  pendulum  started  to  swing  in  a  true  plane. 


FIG.  10.  —  Foucault's  Pendulum  in  the 
Pantheon 


THE  EARTH'S  ROTATION  83 

But  this  plane  at  once  began  to  deviate  slowly  towards 
the  right,  so  that  the  pin  on  the  pendulum  ball  cut  the 
sand  ridge  in  a  new  place  at  each  swing,  shifting  at  a  rate 
which  would  carry  the  line  fully  around  in  about  thirty- 
two  hours,  if  the  pendulum  did  not  first  come  to  rest.  In 
fact,  the  floor  was  actually  and  visibly  turning  under  the 
plane  defined  by  the  swinging  of  the  pendulum. 

The  experiment  created  great  enthusiasm  at  the  time  and  has  since 
been  frequently  performed  (in  Paris,  very  recently).  The  pendulum 
used  in  such  experiments  must,  in  order  to  secure  success,  have  a 
round  ball,  must  be  suspended  by  a  round  wire  or  on  a  point,  and 
must  be  very  heavy,  very  long,  and  very  carefully  protected  against 
currents  of  wind.  At  the  pole  the  plane  of  the  pendulum  will  shift 
completely  around  once  in  twenty-four  hours ;  at  the  equator  it  will 
not  turn  at  all;  and  in  the  intermediate  regions  it  will  shift  more 
or  less  rapidly  according  to  the  latitude  of  the  place  where  the 
experiment  is  performed.  (For  fuller  description,  see  General 
Astronomy,  Arts.  140  and  141.) 

There  are  a  number  of  other  experimental  proofs  of  the  earth's 
rotation,  which  are  really  just  as  conclusive  as  the  one  above  cited 
(General  Astronomy,  Arts.  138-144). 

108,    Invariability  of  the   Earth's  Rotation.  — It   is   a 

question  of  great  importance  whether  the  day  ever  changes 
its  length.  Theoretically,  it  must  almost  necessarily  do  so. 
The  friction  of  the  tides  and  the  fall  of  meteors  upon  the 
earth  both  tend  to  retard  the  rotation,  while,  on  the  other 
hand,  the  earth's  loss  of  heat  by  radiation  and  the  conse- 
quent shrinkage  of  the  globe  must  tend  to  accelerate  it, 
and  to  shorten  the  day.  Then  geological  changes,  the 
elevation  and  subsidence  of  continents,  and  the  transporta- 
tion of  soil  by  rivers,  act,  some  one  way  and  some  the 
other.  At  present  we  can  only  say  that  the  change,  if  any 


84 


LESSONS  IN  ASTRONOMY 


change  has  occurred  since  Astronomy  became  accurate,  has 
been  too  small  to  be  detected.  The  day  is  certainly  not 
longer  or  shorter  by  the  ^  part  of  a  second  than  it  was 
in  the  days  of  Ptolemy;  probably  it  has  not  changed  by 
the  TliW  Part  of  a  second,  though  of  that  we  can  hardly 
be  sure. 

109.  Shiftings  of  the  Earth's  Axis Theoretically,  any  changes 

in  the  distribution  of  materials  within  or  upon  the  globe  of  the  earth 
ought  to  produce  corresponding  displacements  of  the  axis,  and  these 

would  principally  show 
themselves  as  variations  in 
the  latitudes  and  longitudes 
of  observatories.  The  actual 
variations  are  so  minute, 
however,  that  it  is  only  as 
recently  as  1889  that  they 
were  first  clearly  detected  by 
certain  German  observers, 
whose  results  have  since  been 
abundantly  confirmed  and 

FIG.  11.  -  Effect  of  Earth's  Rotation  on  its     extended-    Jt  w  now  beyond 

Form  doubt  that  the  earth  really 

"wobbles"  in  whirling;  and 

this  causes  each  pole  to  describe  an  apparently  irregular  path  around 
its  mean  position,  never  departing  from  it,  however,  by  more  than 
forty  or  fifty  feet.  Dr.  Chandler  has  shown  that  this  motion  is  com- 
pounded of  two  :  one  oval,  with  a  period  of  a  year ;  the  other  circular, 
with  a  period  of  428  days. 

To  explain  certain  geological  phenomena  it  has  been  surmised  that 
great  and  permanent  displacements  of  the  poles  have  occurred  in  the 
distant  past.  But  of  this  we  have,  as  yet,  no  satisfactory  evidence. 

110.  Effect  of  the  Earth's  Rotation  on  its  Form.  —  The 
whirling  of  the  earth  on  its  axis  tends  to  make  the  globe 
bulge  at  the  equator  and  flatten  at  the  poles,  in  the  way 


THE   EARTH'S  FORM  85 

illustrated  by  the  well-known  little  apparatus  shown  in 
Fig.  11.  That  the  equator  does  really  bulge  in  this  way 
is  shown  by  measuring  the  length  of  a  degree  of  latitude 
on  the  various  parts  of  the  earths  surface  between  the  equator 
and  the  pole,  in  the  manner  indicated  a  few  pages  back 
(Sec.  105).  More  than  twenty  such  arcs  have  been  meas- 
ured, and  it  appears  that  the  length  of  the  degrees  increases 
regularly  from  the  equator  towards  the  poles,  as  shown  in 
the  following  table  : 


equator,  one  degree  =  68.704  miles. 

AUat.  20°  »  «  =68.786  « 

"  "  40°  "  "  =  68.993  " 

«  "  60°  "  "  =  69.230  « 

«  «  80°  «  "  =  69.386  " 

At  the  pole,          "         «       =  69.407      « 

The  difference  between  the  equatorial  and  polar  degree 
of  latitude  is  more  than  0.7  of  a  mile,  or  over  3700  feet, 
while  the  probable  error  of  measurement  cannot  exceed  a 
foot  or  two  to  the  degree. 

From  this  .table  it  can  be  calculated,  by  methods  which 
cannot  be  explained  without  assuming  too  much  mathe- 
matical knowledge  in  our  readers,  that  the  earth  is  Qrange- 
shaped,  or  "an  oblate  spheroid,"  the  diameter  from  pole 
to  pole  being  7899.74  miles,  while  the  equatorial  diameter 
is  7926.61  miles.  The  difference,  26.87  miles,  is  about  ^ 
of  the  equatorial  diameter.  This  fraction,  ^^,  is  called 
the  ollateness,  or  ellipticity,  of  the  earth. 

Students  are  often  puzzled  by  the  fact  that  although  the  pole  is 
nearer  the  center  of  the  earth  than  the  equator,  yet  the  degrees  of 
latitude  are  longest  at  the  pole.  It  is  because  the  earth's  surface 


86 


LESSONS  IN  ASTRONOMY 


there  is  more  nearly  flat  than  anywhere  else,  so  that  a  person  has  to 
travel  more  miles  to  change  the  direction  of  his  plumb-line  one 
degree.  Fig.  12  illustrates  this.  The  angles  adb  audfhy  are  equal, 
but  the  arc  ab  is  longer  than  fg. 

111.  Effect  of  the  Earth's  Rotation  and  Ellipticity  upon 
the  Force  of  Gravity.  —  For  two  reasons  the  force  of  gravity 
is  less  at  the  equator  than  at  the  poles.  (1)  The  surface 
of  the  earth  is  there  thirteen  and  one-half  miles  farther 
from  the  center,  and  this  fact  diminishes  the  gravity  at 
the  equator  by  about  5-^.  ((2)  The  centrifugal  force  of 

the  earth's  rotation 

/&  reduces  the  gravity 

at  the  equator  by 
about  ^-Q ;  the 
whole  reduction, 
therefore  (^^  -j- 

2l*)» is  very  nearly 

equal  to  I^-a  ;  i.e., 
an  object  which 
weighs  190  pounds 
at  the  equator 
would  weigh  191  pounds  near  the  pole,  —  weighed  by  an 
accurate  spring-balance.  (In  an  ordinary  balance  the  loss 
of  weight  would  not  show,  simply  because  the  weights 
themselves  would  be  affected  as  much  as  the  body  weighed, 
so  that  the  balance  would  not  be  disturbed.) 

The  effect  of  this  variation  of  gravity  from  the  pole  to  the 
equator  is  especially  evident  in  the  going  of  a  pendulum 
clock.  Such  a  clock,  adjusted  to  keep  accurate  time  at  the 
equator,  would  gain  3m378  a  day  near  the  pole.  In  fact, 
one  of  the  best  ways  of  determining  the  form  of  the  earth 


FIG.  12.  —  Length  of  Degrees  in  Different 
Latitudes 


THE   EARTH'S  MASS  AND  DENSITY  87 

is  by  experiments  with  a  pendulum  at  stations  which  differ 
considerably  in  latitude. 

112.  Surface  and  Volume  of  the  Earth.  —  The  earth  is 
so  nearly  spherical  that  we  can  compute  its  surface  and 
volume  with  sufficient  accuracy  by  the  formula  for  a  per- 
fect sphere,  provided  we  put  the  earth's  mean  semi-diameter 
for  the  radius  of  the  sphere.     This  mean  semi-diameter  is 
not  the  average  of  the  polar  and  equatorial  diameters,  but 
is  found  by  adding  the  polar  diameter  to  twice  the  equa- 
torial, and  dividing  by  three.     It  comes  out  7917.66  miles. 
From  this  we  find  the  earth's  surface  to  be,  in  round  num- 
bers, 197,000000  square  miles,  and  its  volume,  or  bulk, 
260000,000000  cubic  miles. 

113.  TfceJSarth's  Mass  and  Density.  —  The  volume  (or 
bulk)  of  a  globe  is  simply  the  number  of  cubic  miles  of 
space  which  it  contains.     If  the  earth  were  all  made  of 
feathers  or  of  lead,  its  volume  would  remain  the  same,  as 
long  as  the  diameter  was  not  altered.     The  earth's  mass, 
on  the  other  hand,  is  the  quantity  of  matter  in  it,  —  the 
number  of  tons  of  rock  and  water  which  compose  it,  —  and 
of  course  it  makes  a  great  difference  with  this  whether  the 
material  be  heavy  or  light.     The  density  of  the  earth  is  the 
number  of  times  its  mass  exceeds  that  of  a  sphere  of  pure 
water  having  the  same  dimensions. 

The  methods  by  which  the  mass  of  the  earth  can  be  measured 
depend  upon  a  comparison  between  the  attraction  which  the  earth 
exerts  upon  a  body  at  its  surface  and  the  attraction  which  is  exerted 
upon  the  same  body  by  another  body  of  known  mass  and  at  a  known 
distance.  The  necessary  experiments  are  delicate  and  difficult, 
because  the  attraction  exerted  by  a  body  of  any  manageable  size 
is  extremely  minute.  We  must  refer  for  details  to  our  larger 
book,  General  Astronomy,  Arts.  164-170. 


88  LESSONS  IN  ASTRONOMY 

According  to  the  best  data  at  present  available  the  earth's 
density  is  about  5.53,  and  its  mass  about  6000  millions  of 
millions  of  millions  of  tons. 

Among  the  recent  determinations  the  most  trustworthy 
perhaps  are  those  made  by  Boys  in  England  in  1894,  and 
by  Braun  in  Bohemia  about  the  same  time. 

114.  Constitution  of  the  Earth's  Interior.  —  Since  the 
average  density  of  the  earth's  crust  does  not  exceed  three 
times  that  of  water,  while  the  mean  density  of  the  whole 
earth  is  about  ^5.5^  it  is  clear  that  at  the  earth's  center  the 
density  must  be  very  much  greater  than  at  the  surface. 
Very  likely  it  is  as  high  as  eight  or  ten  times  the  density 
of  water,  and  equal  to  that  of  the  heavier  metals. 

There  is  nothing  surprising  in  this.  If  the  earth  were  once  fluid, 
it  is  natural  to  suppose  that  the  densest  materials,  in  the  process  of 
solidification,  would  settle  towards  the  center. 

Whether  the  center  of  the  earth  is  now  solid  or  fluid,  it  is  difficult 
to  say  with  certainty.  Certain  tidal  phenomena,  to  be  mentioned 
hereafter,  have  led  Sir  William  Thomson  to  conclude  that  the  earth 
as  a  whole  is  solid  throughout,  and  "  more  rigid  than  glass,"  vol- 
canic centers  being  mere  "  pustules,"  so  to  speak,  in  the  general 
mass.  His  conclusions  were  confirmed  by  Michelson  and  Gale  in 
1913. 


EARTH'S  ORBITAL  MOTION  89 

THE   APPARENT   MOTION   OF   THE   SUN  AND   THE 

ORBITAL  MOTION  OF  THE  EARTH,  AND  THEIR 

IMMEDIATE  CONSEQUENCES 

115.  ThejBun's  Apparent  Motion  among  the  Stars.  —  The 
sun's  apparent  motion  among  the  stars,1  which  makes  it 
describe  the  circuit  of  the  heavens  once  a  year,  must  have 
been  among  the  earliest  recognized  astronomical  phenomena, 
as  it  is  one  of  the  most  important.  The  sun,  starting  in 
the  spring,  mounts  northward  in  the  sky  each  day  at  noon 
for  three  months,  appears  to  stand  still  a  few  days  at  the 
summer  solstice,  and  then  descends  towards  the  south,  reach- 
ing in  autumn  the  same  noonday  elevation  which  it  had  in 
the  spring.  It  keeps  on  its  southward  course  to  the  winter 
solstice  (in  December),  and  then  returns  to  its  original 
height  at  the  end  of  a  year,  by  its  course  causing  and 
marking  the  seasons. 

Nor  is  this  all.  The  sun's  motion  is  not  merely  north 
and  south,  but  it  also  advances  continually  eastward  among 
the  stars,  completing  the  circuit  in  a  year.  It  is  true  that 
we  cannot  see  the  stars  near  the  sun  in  the  same  -way  that 
we  can  those  about  the  moon,  so  as  to  be  able  directly  to 
perceive  this  motion;  but  in  the  spring  the  stars  which  are 
rising  in  the  east  at  sunset  are  different  from  those  which 
are  found  there  in  the  summer  or  in  the  winter.  In  March 
the  most  conspicuous  of  the  eastern  constellations  at 
sunset  are  Leo  and  Bootes.  A  little  later  Virgo  appears  ; 
in  the  summer  Ophiuchus  and  Libra;  still  later  Scorpio; 


student  must  carefully  discriminate  between  "motion  among 
the  stars"  and  the  diurnal  motion,  in  which  sun,  moon,  planets,  and 
comets  all  partake  along  with  the  stars. 


90  LESSONS  IN  ASTRONOMY 

while  in  midwinter  Orion  and  Taurus  are  ascending  as  the 
sun  goes  down.  The  combination  of  these  two  motions  in 
declination  and  right  ascension  annually  carries  the  sun 
around  the  heavens  in  the  ecliptic  (Sec.  20). 

So  far  as  the  obvious  appearances  are  concerned,  it  is 
quite  indifferent  whether  we  suppose  the  earth  to  revolve 
around  the  sun,  or  vice  versa.  That  the  earth  really  moves, 
however,  is  absolutely  demonstrated  by  two  phenomena  too 
minute  and  delicate  for  observation  without  the  telescope, 
but  accessible  to  modern  methods.  One  of  them  is  the 
aberration  of  light,  the  other  the  annual  parallax  of  the 
Jixed  stars.  These  can  be  explained  only  by  the  actual 
motion  of  the  earth,  but  we  postpone  their  discussion  for 
the  present.  (See  Sec.  343,  and  Appendix,  Sec.  435.) 

116,  The  Ecliptic;  its  Related  Points  and  Circles.  — By 
observing  daily  with  the  meridian  circle  the  sun's  declina- 
tion and  the  difference  between  its  right  ascension  and 
that  of  some  standard  star,  we  obtain  a  series  of  positions 
of  the  sun's  center  which  can  be  plotted  on  the  globe,  and 
we  can  thus  mark  out  the  path  of  the  sun  among  the  stars. 
It  turns  out  to  be  a  great  circle,  as  is  shown  by'its  cutting 
the  celestial  equator  at  two  points  just  180°  apart  (the 
so-called  "equinoctial  points,"  or  "equinoxes"),  where  it 
makes  an  angle  with  the  equator  of  approximately  23£° 
(23°  27'  08"  in  1900). 

This  great  circle,  already  several  times  referred  to,  is 
•called  the  Ecliptic,  because,  as  was  early  discovered,  eclipses 
happen  only  when  the  moon  is  crossing  it.  Its  position 
among  the  constellations  is  shown  upon  the  equatorial  star- 
maps.  It  may  be  defined  as  the  circle  in  which  the  plane 
of  the  earth's  orbit  cuts  the  celestial  sphere. 


THE  ECLIPTIC  AND  THE  ZODIAC  91 

The  angle  which  the  ecliptic  makes  with  the  equator  at  the  equi- 
noctial points  is  called  the  Obliquity  of  the  Ecliptic.  This  obliquity  is- 
evidently  equal  to  the  sun's  greatest  distance  from  the  equator,  i.e., 
its  maximum  declination  (23°  27'),  which  is  reached  in  December 
and  June. 

117.  The  two  points  in  the  ecliptic  midway  between  the 
equinoxes  are  called  the  Solstices,  because  at  these  points 
the  sun  "stands,"  that  is,  ceases  to  move  north  or  south. 
Two  circles  drawn  through  the  solstices  parallel  to  the 
equator  are  called  the  Tropics,  or  "  turning-lines,"  because 
there  the   sun  turns  from  its  northward  motion  to  the 
southward,  or  vice  versa.     The  two  points  in  the  heavens 
90°  distant  from  the  ecliptic  are  called  the  Poles  of  the 
Ecliptic.    The  northern  one  is  in  the  constellation  of  Draco, 
about  midway  between  the  stars  Delta  and  Zeta  Draconis, 
at  a  distance  from  the  pole  of  the  heavens  equal  to  the 
obliquity  of  the  ecliptic,  and  on  the  Solstitial  Colure,  the 
hour-circle  which  runs  through  the  two  solstices ;  the  hour- 
circle  which  passes  through  the  equinoxes  being  called  the 
Equinoctial  Colure.     Great  circles  drawn  through  the  poles 
of  the  ecliptic,  and  therefore  perpendicular,  or  "second- 
aries," to  the  ecliptic,  are  known  as  "circles  of  latitude." 
It  will  be  remembered  (Sec.  20)  that  celestial  longitude  and 
latitude  are  measured  with  reference  to  the  ecliptic,  and 
not  to  the  equator. 

118.  The  Zodiac  and  its  Signs.  — A  belt  16°  wide  (8° 
on  each  side  of  the  ecliptic)  is  called  the  Zodiac,  or  zone 
of  animals,  the  constellations  in  it,  excepting  Libra,  being 
all   figures    of   animals.     It   is   taken   of   that  particular 
width    simply   because    the    moon   and  all  the  principal 
planets  always  keep  within  it.     It  is  divided   into   the 


LESSONS  IN  ASTRONOMY 


so-called  signs,  each  30°  in  length,  having  the  following 
names  and  symbols : 


Spring 


f  Aries 
<j  Taurus 
L  Gemini 
f  Cancer 
Summer   •<  Leo 


[Virgo 


fLibra  =£= 

Au tuning  Scorpio          TT^ 
^Sagittarius    f 

TCapricornus  V? 
Winter   <  Aquarius      sxx 

[  Pisces  x 


The  symbols  are  for  the  most  part  conventionalized  pictures  of 
the  objects.  The  symbol  for  Aquarius  is  the  Egyptian  character  for 
water.  The  origin  of  the  signs  for  Leo,  Capricornus,  and  Virgo  is 
not  quite  clear. 

The  zodiac  is  of  extreme  antiquity.  In  the  zodiacs  of 
the  earliest  history  the  Fishes,  Ram,  Bull,  Lion,  and 
Scorpion  appear  precisely  as  now. 

119.  The  Earth's  Orbit.  —  The  ecliptic  must  not  be  con- 
founded with  the  earth's  orbit.  It  is  simply  a  great  circle 
of  the  infinite  celestial  sphere,  —  the  trace  made  upon  that 
sphere  by  the  plane  of  the  earth's  orbit,  which  is  its  path 
in  space.  The  fact  that  the  ecliptic  is  a  great  circle  gives 
us  no  information  about  the  earth's  orbit  itself,  except 
that  it  lies  in  a  plane  passing  through  the  sun.  It  tells  us 
nothing  as  to  the  orbit's  real  form  and  size. 

By  reducing  the  observations  of  the  sun's  right  ascension 
and  declination  through  the  year  to  longitude  and  latitude 
(the  latitude  would  always  be  exactly  zero  except  for  some 
slight  perturbations  due  chiefly  to  the  moon's  revolution 
around  the  earth),  and  combining  these  data  with  observa- 
tions of  the  sun's  apparent  diameter,  we  can,  however, 
ascertain  the  form  of  the  earth's  orbit  and  the  law  of  its 


THE  EARTH'S   ORBIT 


93 


motion.     (The  size  of  the  earth's  orbit,  i.e.,  its  scale   of 
miles,  cannot  be  fixed  until  we  find  the  sun's  distance.) 

The  result  is  that  the  orbit  is  found  to  be  very  nearly  a 
circle,  but  not  exactly  so.  It  is  an  oval  or  ellipse,  with 
the  sun  at  one  of  its  foci  (as  illustrated  in  Fig.  13),  but  is 
much  more  nearly  circular  than  the  oval  there  represented. 
Its  eccentricity  is  only  about  ^ ;  that  is  to  say,  the  dis- 
tance from  the  center  of  the  sun  to  the  middle  of 
ellipse  is  only  about  g1^  of 
the  average  distance  of  the 
sun  from  the  earth. 

The  method  by  which 
we  proceed  to  ascertain  the 
form  of  the  orbit  may  be 
found  in  the  Appendix, 


the 


FIG.  13.  —  The  Ellipse 


Sec.  428.  (For  a  description 
of  the  ellipse,  see  Sec.  429.) 

120.  Definition  of  Terms. 

—  The  points  where  the  earth  is  nearest  to  and  most 
remote  from  the  sun  are  called  respectively  the  Perihelion 
and  the  Aphelion  (December  31  and  June  30),  the  line 
joining  them  being  the  major  axis  of  the  orbit.  This  line, 
indefinitely  produced  in  both  directions,  is  called  the 
Line  of  Apsides  (pronounced  Ap'si-deez),  the  major  axis 
being  a  limited  piece  of  it.  A  line  drawn  from  the  sun  to 
the  earth,  or  to  any  other  planet  at  any  point  in  its  orbit, 
as  SP  in  Fig.  13,  is  called  the  planet's  Radius  Vector. 

The  variations  in  the  sun's  apparent  diameter  due  to  our 
changing  distance  are  too  small  to  be  detected  without  a 
telescope,  so  that  the  ancients  failed  to  perceive  them. 
Hipparchus,  however,  about  120  B.C.  discovered  that  the 


94  LESSONS  IN  ASTRONOMY 

earth  is  not  in  the  center1  of  the  circular  orbit  which  he  sup- 
posed the  sun  to  describe  around  it  with  uniform  velocity. 
Obviously  the  sun's  apparent  motion  is  not  uniform, 
because  it  takes  186  days  for  the  sun  to  pass  from  the 
vernal  equinox,  March  20,  to  the  autumnal,  September  22, 
and  only  179  days  to  return.  Hipparchus  explained  this 
on  the  hypothesis  that  the  earth  is  out  of  the  center  of  the 
circle. 

121.  The  Law  of  the  Earth's  Motion.  —  By  combining 
the  measured  apparent  diameter  of  the  sun  with  the  differ- 
ences of  longitude  from  day 
to  day  we  can  deduce  mathe- 
matically not  only  the  form 
of  the  earth's  orbit,  but  the 
law  of  her  motion  in  it.  It 
can  be  shown  from  the  com- 
parison that  the  earth  moves 
in  such  a  way  that  its  radius 
FIG.  14.  —  Equable  Description  of  vector  describes  areas  propor- 
tional to  the  time,  a  law  which 

Kepler  first  brought  to  light  in  1609 ;  that  is  to  say,  if  ab, 
cd,  and  ef  (Fig.  14)  be  portions  of  the  orbit  described  by  the 
earth  in  different  weeks,  the  areas  of  the  elliptical  sectors 
aSb,  cSd,  and  eSf  are  all  equal.  A  planet  near  perihelion 
moves  faster  than  at  aphelion  in  just  such  proportion  as 
to  preserve  this  relation. 

As  Kepler  left  the  matter,  this  is  a  mere  fact  of  obser- 
vation. Newton  afterwards  proved  that  it  is  the  necessary 

1  Hipparchus  (and  every  one  else  until  the  time  of  Kepler,  1607) 
assumed  on  metaphysical  grounds  that  the  sun's  orbit  must  necessarily 
be  a  circle,  and  described  with  a  uniform  motion. 


CHANGES  IN  THE  EARTH'S  ORBIT  95 

mechanical  consequence  of  the  fact  that  the  earth  moves 
under  the  action  of  a  force  always  directed  towards  the  sun. 

It  is  true  in  every  case  of  the  elliptical  motion  of  a  heavenly 
body,  and  enables  us  to  find  the  position  of  the  earth  or  of  any  planet, 
when  we  once  know  the  time  of  its  orbital  revolution  (technically 
the  "period")  and  the  time  when  it  was  last  at  perihelion.  The 
solution  of  the  problem,  first  worked  out  by  Kepler,  lies,  however, 
quite  beyond  the  scope  of  the  present  work. 

122.  Changes  in  the  Earth's  Orbit.  —  The  orbit  of  the 
earth  changes  slowly  in  form  and  position,  though  in  the 
long  run  it  is  unchangeable  as  regards  the  length  of  its 
major  axis  and  the  duration  of  the  year. 

These  so-called  "secular  changes"  are  due  to  "pertur- 
bations "  caused  by  the  action  of  the  other  planets  upon 
the  earth.  Were  it  not  for  their  attraction  the  earth  would 
keep  her  orbit  with  reference  to  the  sun  and  stars  abso- 
lutely unaltered  from  age  to  age. 

Besides  these  secular  perturbations  of  the  earth's  orbit, 
the  earth  itself  is  also  continually  being  slightly  disturbed 
in  its  orbit.  On  account  of  its  connection  with  the  moon 
it  oscillates  each  month  a  few  hundred  miles  above  and 
below  the  true  plane  of  the  ecliptic,  and  by  the  action  of 
the  other  planets  is  sometimes  set  backwards  or  forwards 
in  its  orbit  to  the  extent  of  some  thousands  of  miles.  Of 
course  every  such  displacement  of  the  earth  produces  a 
corresponding  slight  change  in  the  apparent  position  of 
the  sun  and  of  the  nearer  planets. 

123,  The  Seasons.  —  The  earth  in  its  motion  around  the 
sun  always  keeps  its  axis  nearly  parallel  to  itself  during 
the  whole  year,  for  the  mechanical  reason  that  a  spinning 
globe  maintains  the  direction  of  its  axis  invariable,  unless 


96 


LESSONS  IN  ASTRONOMY 


disturbed  by  some  outside  force  (very  prettily  illustrated 
by  the  gyroscope).  Fig.  15  shows  the  way  in  which  the 
north  pole  of  the  earth  is  tipped  with  reference  to  the  sun 
at  different  seasons  of  the  year.  At  the  vernal  equinox 
(March  20)  the  earth  is  situated  so  that  the  plane  of  its 
equator  passes  through  the  sun.  At  that  time,  therefore, 
the  circle  which  bounds  the  illuminated  portion  of  the 
earth  passes  through  the  two  poles,  as  shown  in  Fig.  16,  B, 

Autumnal  Equinox 


Vernal  Equinox 

FIG.  15.  — The  Seasons 

and  day  and  night  are  therefore  equal,  as  implied  by  the 
term  "  equinox."  The  same  is  again  true  on  the  22d  of 
September.  About  the  21st  of  June  the  earth  is  so  situ- 
ated that  its  north  pole  is  inclined  towards  the  sun  by 
about  23|°,  as  shown  in  Fig.  16,  A.  The  south  pole  is 
then  in  the  unlighted  half  of  the  earth's  globe,  while  the 
north  pole  receives  sunlight  all  day  long,  and  in  all  por- 
tions of  the  northern  hemisphere  the  day  is  longer  than 


THE  SEASONS  97 

the  night.  In  the  southern  hemisphere,  on  the  other  hand, 
the  reverse  is  true. 

At  the  time  of  the  winter  solstice  the  southern  pole  has 
continual  sunshine,  and  the  north  pole  is  in  the  night. 

At  the  equator  of  the  earth  day  and  night  are  equal  at 
all  times  of  the  year,  and  at  that  part  of  the  earth  there 
are  no  seasons  in  the  proper  sense  of  the  word,  though 
there  are  usually  alternations  of  rain  and  drought  due  to 
changes  in  the  direction  of  the  winds.  Everywhere  else 
the  day  and  night  are  unequal, 
except  when  the  sun  is  at  one 
of  the  equinoxes. 

In  high  latitudes  the  inequal- 
ity between  the  lengths  of  the 
day  in  summer  and  in  winter 
is  Very  great;  and  at  places  FIG.  16,- Position  of  Pole  at 

Solstice  and  Equinox 

within    the   polar   circle   there 

are  always  days  in  winter  when  the  sun  does  not  rise  at 
all,  and  others  in  the  summer  when  it  does  not  set,  but 
exhibits  the  phenomenon  of  the  "midnight  sun,"  as 
already  explained  in  Sec.  86.  At  the  pole  itself  the 
summer  is  one  perpetual  day,  six  months  in  length,  while 
the  winter  is  a  six-months  night. 

Perhaps  the  student  will  get  a  better  idea  by  thinking  of  the  earth 
as  a  globe  floating,  just  half  immersed,  on  a  sheet  of  still  water,  and 
so  weighted  that  its  poles  dip  at  an  angle  of  23^°,  while  it  swims  in 
a  circle  around  the  sun,  a  much  larger  globe,  also  floating  on  the 
same  surface.  The  sheet  of  water  corresponds  to  the  ecliptic,  while 
the  plane  of  the  equator  is  a  circle  on  the  globe  itself,  drawn  square 
to  the  axis.  If  now  the  axis  is  kept  pointing  always  the  same  way 
(always  north,  for  instance),  while  the  globe  swims  around,  things 
will  correspond  to  the  motion  of  the  earth  around  the  sun. 


98  LESSONS  IN  ASTRONOMY 

124,  Effects  on  Temperature.  —  The  changes  in  the  dura- 
tion of  insolation  (exposure  to  sunshine)  at  any  place  involve 
changes  of  temperature,  thus  producing  the  seasons.  It  is 
clear  that  the  surface  of  the  soil  at  any  place  in  the  north- 
ern hemisphere  will  receive  daily  from  the  sun  more  than 
the  average  amount  of  heat  whenever  he  is  north  of  the 
celestial  equator,  and  for  two  reasons : 

1.  Sunshine  lasts  more  than  half  the  day. 

2.  The  mean  altitude  of  the  sun  during  the  day  is  greater 
than  the  daily  average  for  the  year,  since  he  is  higher  at 

noon  than  at  the  time  of  the 
equinox,  and  in  any  case 
reaches  the  horizon  at  rising 
and  setting. 

Now    the    more    obliquely 
the  rays  strike,  the  less  heat 
they    bring    to    each    square 
FIG.  17. -Effect  of  Sun's  Elevation  inch  of  surface,  as  is  obvious 

on  Amount  of  Heat  imparted  to   from  Fig.  17.     A  beam  of  SU11- 

shine  which  would  cover  the 

surface  AC,  if  received  squarely,  will  be  spread  over  a 
much  larger  surface,  Ac,  if  it  falls  at  the  angle  h.  The 
difference  in  favor  of  vertical  rays  is  further  exaggerated 
by  the  absorption  of  heat  in  our  atmosphere,  because  the 
rays  that  are  nearly  horizontal  have  to  traverse  a  much 
greater  thickness  of  air  before  reaching  the  ground. 

For  these  two  reasons,  therefore,  the  temperature  rises 
rapidly  for  a  place  in  the  northern  hemisphere  as  the  sun 
comes  north  of  the  equator.  We,  of  course,  receive  the 
most  heat  in  twenty-four  hours  at  the  time  of  the  summer 
solstice ;  but  this  is  not  the  hottest  time  of  the  summer. 


PRECESSION  99 

The  weather  is  then  getting  hotter,  and  the  maximum 
will  not  be  reached  until  the  increase  ceases,  i.e.,  not 
until  the  amount  of  heat  lost  in  twenty-four  hours  equals 
that  received  in  the  same  time.  This  maximum  is  reached 
in  our  latitude  about  the  1st  of  August.  For  similar 
reasons  the  minimum  temperature  in  winter  occurs  about 
February  1. 

125,    Precession  of  the  Equinoxes.  — 


ward  motion  of  the  equinoxes  along  the  ecliptic.  In  explain- 
ing the  seasons  we  have  said  (Sec.  123)  that  the  earth  keeps 
its  axis  nearly  parallel  to  itself  during  its  annual  revolu- 
tion. It  does  not  maintain  strict  parallelism,  however  ;  but 
owing  to  the  attraction  of  the  sun  and  moon  on  that  portion 
of  the  mass  of  the  earth  which  projects,  like  an  equatorial 
ring,  beyond  the  true  spherical  surface,  the  earth's  axis 
continually  but  slowly  shifts  its  place,  keeping  always 
nearly  the  same  inclination  to  the  plane  of  the  ecliptic,  so 
that  its  pole  revolves  in  a  small  circle  of  23£°  radius  around 
the  pole  of  the  ecliptic  once  in  25,800  years.  Of  course 
the  celestial  equator  must  move  also,  since  it  has  to  keep 
everywhere  just  90°  from  the  celestial  pole  ;  and,  as  a 
consequence,  the  equinoxes  move  westward  on  the  ecliptic 
about  50".  2  each  year,  as  if  to  meet  the  sun.  This  motion 
of  the  equinox  was  called  "  precession"  by  Hipparchus,  who 
discovered1  it  about  125  B.C.,  but  could  not  explain  it. 
The  explanation  was  not  reached  until  the  time  of  Newton, 
about  200  years  ago,  who  showed  it  to  be  a  necessary  result 
of  gravitation  operating  under  the  actual  conditions. 

1  He  discovered  it  by  finding  that  in  his  time  the  place  of  the  equinox 
among  the  stars  was  no  longer  the  same  that  it  used  to  be  in  the  days  of 
Homer  and  Hesiod,  several  hundred  years  before. 


100  LESSONS  IN  ASTRONOMY 

126.    Effect  of  Precession  upon  the  Pole  and  the  Zodiac.  — 

At  present  the  Pole-star,  Alpha  Ursse  Minoris,  is  about 
li°  from  the  pole,  while  in  the  time  of  Hipparchus  the 
distance  was  fully  12°.  During  the  next  two  centuries 
the  distance  will  diminish  to  about  30',  and  then  begin  to 
increase. 

If  upon  the  celestial  globe  we  trace  a  circle  of  23£° 
radius  around  the  pole  of  the  ecliptic  as  a  center,  it  will 
mark  very  nearly  the  track  of  the  celestial  pole  among 
the  stars. 

Other  causes  slightly  shift  the  position  of  the  ecliptic  and  its  pole, 
so  that  the  actual  path  of  the  pole  among  the  stars  deviates  sensibly 
from  an  exact  circle. 

It  passes  not  very  far  from  Alpha  Lyrse  (Vega),  on  the  opposite 
side  of  the  circle  from  the  present  Pole-star ;  about  12,000  years  hence 
Vega  will,  therefore,  be  the  Pole-star.  Reckoning  backwards,  we 
find  that  some  4000  years  ago  Alpha  Draconis  (Thuban)  was  the 
Pole-star,  and  about  3£°  from  the  pole. 

Another  effect  of  precession  is  that  the  signs  of  the 
zodiac  do  not  now  agree  with  the  constellations,  which 
bear  the  same  name.  The  sign  of  Aries  is  now  in  the 
constellation  of  Pisces,  and  so  on,  each  sign  having 
"backed"  bodily,  so  to  speak,  into  the  constellation  west 
of  it. 

The  forces  which  cause  precession  do  not  act  quite  uni- 
formly, and  as  a  result  the  rapidity  of  the  precession  varies 
somewhat,  and  there  is  also  a  slight  tipping  or  nodding  of 
the  earth's  axis,  which  is  called  nutation.  (For  a  fuller 
account  of  the  whole  matter,  see  General  Astronomy, 
Arts.  209-215.) 


EARTH'S  ORBITAL  '^MOTION  101 

THE  YEAR  AND  THE  CALENDAR 

127.  Three  different  kinds  of  "year"  are  now  recog- 
nized,—  the   Sidereal,  the   Tropical  (or  Equinoctial),  and 
the  Anomalistic. 

The  sidereal  year,  as  its  name  implies,  is  the  time 
occupied  by  the  sun  in  apparently  completing  the  circuit 
from  a  given  star  to  the  same  star  again.  Its  length  is 
365d6h9m98.  From  the  mechanical  point  of  view  this  is 
the  true  year,  i.e.,  it  is  the  time  occupied  by  the  earth  in 
completing  its  revolution  around  the  sun  from  a  given 
direction  in  space  to  the  same  direction  again. 

The  tropical  year  is  the  time  included  between  two  suc- 
cessive passages  of  the  vernal  equinox  by  the  sun.  Since 
the  equinox  moves  yearly  50". 2  towards  the  west,  the  trop- 
ical year  is  shorter  than  the  sidereal  by  about  twenty  minutes, 
its  length  being  365d5h48m468.  Since  the  seasons  depend 
on  the  surfs  place  with  respect  to  the  equinox,  the  tropical 
year  is  the  year  of  chronology  and  civil  reckoning. 

The  third  kind  of  year  is  the  anomalistic  year,  —  the  time  between 
two  successive  passages  of  the  perihelion  by  the  earth.  Since  the 
line  of  apsides  of  the  earth's  orbit  makes  an  eastward  revolution  once 
in  about  108,000  years,  this  kind  of  year  is  nearly  five  minutes  longer 
than  the  sidereal,  its  length  being  365d6h13m488.  It  is  but  little  used 
except  in  calculations  relating  to  perturbations  of  the  planets. 

128.  The  Calendar.  —  The  natural  units  of  time  are  the 
day,  the  month,  and  the  year.     The  day  is  too  short  for 
convenience  in  dealing  with  considerable  periods,  such  as 
the  life  of  a  man,  for  instance ;  and  the  same  is  true  even 
of  the  month;  so  that  for  all  chronological  purposes  the 
tropical  year  (the  year  of  the  seasons)  has  always  been 


102  LESSONS  IN  ASTRONOMY 

employed.  At  the  same  time,  so  many  religious  ideas  and 
observations  have  been  connected  with  the  changes  of  the 
moon  that  there  has  been  a  constant  struggle  to  reconcile 
the  month  with  the  year.  Since  the  two  are  incommen- 
surable, no  really  satisfactory  solution  is  possible,  and  the 
modern  calendar  of  civilized  nations  entirely  disregards  the 
lunar  phases.  In  early  times  the  calendar  was  in  the  hands 
of  the  priesthood  and  was  mainly  lunar,  the  seasons  being 
either  disregarded  or  kept  roughly  in  place  by  the  occa- 
sional putting  in  or  dropping  of  a  month.  The  Moham- 
medans still  use  a  purely  lunar  calendar,  having  a  "  year  " 
of  twelve  months,  which  contains  alternately  354  and  365 
days.  In  their  reckoning  the  seasons  fall  continually  in 
different  months,  and  their  calendar  gains  on  ours  about 
one  year  in  thirty-three.  » 

129.  The  Julian  Calendar. — When  Julius  Caesar  came 
into  power  he  found  the  Roman  calendar  in  a  state  of 
hopeless  confusion.  He,  therefore,  with  the  advice  of 
Sosigenes,  the  astronomer,  established  (45  B.C.)  what  is 
known  as  the  Julian  calendar,  which  still,  either  untouched 
or  with  a  trifling  modification,  continues  in  use  among  civil- 
ized nations.  Sosigenes  discarded  all  reference  to  the 
moon's  phases,  and  adopting  365i  days  as  the  true 
length  of  the  year,  he  ordained  that  every  fourth  year 
should  contain  366  days,  —  the  extra  day  being  inserted 
by  repeating  the  sixth  day  before  the  Calends  of  March 
(whence  such  a  year  is  called  "  Bissextile ").  He  also 
transferred  the  beginning  of  the  year,  which  before  Caesar's 
time  had  been  in  March  (as  is  indicated  by  the  names  of 
several  of  the  months,  —  December,  the  tenth  month,  for 
instance),  to  January  1. 


THE  CALENDAR  103 

Caesar  also  took  possession  of  the  month  Quintilis,  naming  it 
July  after  himself.  His  successor,  Augustus,  in  a  similar  manner 
appropriated  the  next  month,  Sextilis,  calling  it  August,  and  to  vin- 
dicate his  dignity  and  make  his  month  as  long  as  his  predecessor's 
he  added  to  it  a  day  stolen  from  February. 

The  Julian  calendar  is  still  used  unmodified  in  the 
Greek  Church,  and  also  in  many  astronomical  reckonings. 

130.  The  Gregorian  Calendar.  —  The  true  length  of  the 
tropical  year  is  not  365i  days,  but  365d5h48m46s,  leaving 
a  difference  of  Ilm14s  by  which  the  Julian  year  is  too 
long.  This  difference  amounts  to  a  little  more  than  three 
days  in  400  years.  As  a  consequence  the  date  of  the 
vernal  equinox  comes  continually  earlier  and  earlier  in 
the  Julian  calendar,  and  in  1582  it  had  fallen  back  to 
the  llth  of  March  instead  of  occurring  on  the  21st  as  it, 
did  at  the  time  of  the  Council  of  Nice  (A.D.  325). 
3  Pope  Gregory,  therefore,  under  the  astronomical  advice 
of  Clavius,  ordered  that  the  calendar  should  be  restored  by 
adding  ten  days,  so  that  the  day  following  Oct.  4,  1582, 
should  be  called  the  15th  instead  of  the  5th;  further,  to 
prevent  any  future  displacement  of  the  equinox,  he  decreed 
that  thereafter  only  such  century  years  should  be  leap  years 
as  are  divisible  by  400.  Thus,  1700, 1800, 1900,  and  2100 
are  not  leap  years,  but  1600  and  2000  are. 

The  change  was  immediately  adopted  by  all  Catholic 
countries,  but  the  Greek  Church  and  most  Protestant 
nations  refused  to  recognize  the  pope's  authority.  The  new 
calendar  was,  however,  at  last  adopted  in  England  in  1752, 
so  that  now  the  "  old  style  "  is  used  only  in  Russia  and 
Greece,  and  a  few  other  minor  nations  of  eastern  Europe. 
At  present  (since  the  years  1800  and  1900  were  leap  years- 


104  LESSONS  IN  ASTRONOMY 

in  the  Julian  calendar  and  not  in  the  Gregorian)  the  differ- 
ence between  the  two  calendars  is  thirteen  days. 

In  1900  there  was  a  good  deal  of  discussion  about 
the  beginning  of  the  twentieth  century.  According  to  the 
accepted  chronological  method  of  reckoning,  the  begin- 
ning of  the  Christian  era  is  reckoned  from  the  beginning 
of  the  year  A.D.  1,  the  year  preceding  being  1  B.C.,  with 
no  intervening  year  "zero."  It  follows  that  the  first 
century  was  not  completed  until  the  end  of  the  year 
A.D.  100,  and  that  the  second  century  began  with  A.D.  101, 
as  the  twentieth  did  with  the  year  1901. 

Certain  chronologers  about  two  hundred  years  ago  tried 
to  reform  the  method  of  reckoning  by  inserting  a  year 
A.D.  0  as  the  beginning  of  the  Christian  era,  and  the  plan 
would  offer  some  slight  advantages.  It  did  not,  however, 
meet  with  any  general  acceptance,  though  it  was  for  a  time 
adopted  in  a  few  astronomical  books  and  tables. 


CHAPTER  V 

THE  MOON 

Her  Orbital  Motion  and  the  Month  — Distance,  Dimensions,  Mass,  Density, 
and  Force  of  Gravity  —  Rotation  and  Librations  — Phases— Light  and 
Heat  —  Physical  Condition  —  Telescopic  Aspect  and  Peculiarities  of  the 
Lunar  Surface 

131.  Next  to  the  sun,  the  moon  is  the  most  conspicuous 
and  to  us  the  most  important,  of  the  heavenly  bodies  ;  in 
fact,  she  is  the  only  one  except  the  sun  which  exerts  the 
slightest  perceptible  influence  upon  the  interests  of  human 
life.     She  owes  her  conspicuousness  and  her  importance, 
however,  solely  to  her  nearness;  for  she  is  really  a  very 
insignificant  body  as  compared  with  stars  and  planets. 

132.  The  Moon's  Apparent  Motion ;  Definition  of  Terms, 
etc.  —  One  of  the  earliest  observed  of  astronomical  phe- 
nomena must  have  been  the  eastward  motion  of  the  moon 
with  reference  to  the  sun  and  stars,  and  the  accompany- 
ing change  of  phase.     If,  for  instance,  we  note  the  moon 
to-night  as  very  near  some  conspicuous  star,  we  shall  find 
her  to-morrow  night  at  a  point  considerably  farther  east, 
and  the  next  night  farther  yet;    she  changes  her  place 
about  13°  daily,  and  makes  the  complete  circuit  of  the 
heavens,  from  star  to  star  again,  in  about  2Yi  days.     In 
other  words,  she  revolves  around  the  earth  in  that  time, 
while  she  accompanies  us  in  our  .annual  journey  around 
the  sun.     Since  the  moon  moves  eastward  among  the  stars 
so  much  faster  than  the  sun  (which  takes  a  year  in  going 

105 


106  LESSONS  IN  ASTRONOMY 

once  around),  she  overtakes  and  passes  him  at  regular 
intervals;  and  as  her  phases  depend  upon  her  apparent 
position  with  reference  to  the  sun,  this  interval  from  new 
moon  to  new  moon  is  specially  noticeable,  and  is  what  we 
ordinarily  understand  as  the  "  month." 

The  angular  distance  of  the  moon  east  or  west  of  the  sun 
at  any  time  is  called  her  Elongation.  At  new  moon  it  is  zero, 
and  the  moon  is  said  to  be  in  Conjunction.  At  full  moon 
the  elongation  is  180°,  and  she  is  said  to  be  in  Opposition. 
In  either  case  the  moon  is  in  Syzygy.  (Syzygy  means  "  yoked 
together,"  the  sun,  moon,  and  earth  being  then  nearly  inline.) 
When  the  elongation  is  90°  she  is  said  to  be  in  Quadrature. 

133.  Sidereal  and  Synodic  Months.  —  The  sidereal  month 
is  the  time  it  takes  the  moon  to  make  her  revolution  from 
a  given  star  to  the  same  star  again;  its  length  is  271  days 
(27d7h43mll8.524).  The  mean  daily  motion,  therefore,  is 
360°  divided  by  this,  or  13°  11'  (nearly).  The  sidereal 
month  is  the  true  month  from  the  mechanical  point  of 
view.  On  account  of  "  perturbations,"  it  varies  in  length 
by  as  much  as  three  hours  from  time  to  time. 

The  synodic  month  is  the  time  between  two  successive 
conjunctions  or  oppositions;  i.e.,  between  two  successive 
new  or  full  moons.  Its  average  length  is  about  29£  days 
<29d12h44m28.841),  but  it  varies  nearly  thirteen  hours, 
mainly  on  account  of  the  eccentricity  of  the  moon's  orbit. 

If  M  be  the  mean  length  of  the  moon's  sidereal  period  in  days, 
E  the  length  of  the  sidereal  year,  and  S  the  mean  length  of  the 
synodic  month,  the  three  quantities  are  connected  by  a  simple  relation 

easily  demonstrated.     —  is  the  fraction  of  a  circumference  moved 
M 

over  by  the  moon  in  a  day.     Similarly,  —  is  the  apparent  daily  motion 

E 


THE  MOON'S  PATH  107 

of  the  sun.  The  difference  is  the  amount  which  the  moon  gains  on 
the  sun  daily.  Now  it  gains  a  whole  revolution  in  one  synodic 

month   of  S  days,  and  therefore  must  gain  daily  —  of  a  circum- 

o 

ference.     Hence  we  have  the  important  equation 

JL_I-I 
M~E~~S' 

which  is  known  as  the  equation  of  synodic  motion.  In  a  sidereal 
year  the  number  of  sidereal  months  is  exactly  one  greater  than  the 
number  of  synodic  months,  the  numbers  being  respectively  13.309  + 
and  12.369  +. 

134.  The  Moon's  Path  among  the  Stars.  —  By  observing 
the   moon's  right   ascension  and   declination    daily  with 
suitable  instruments  we  can  map  out  its  apparent  path, 
just  as  in  the  case  of  the  sun  (Sec.  116).     This  path  turns 
out  to  be  (very  nearly)  a  great  circle,  inclined  to  the  eclip- 
tic at  a  slightly  variable  angle  of  about  5°  8'.     The  two 
points  where  it  cuts  the  ecliptic  are  called  the  "nodes," 
the  ascending  node  being  where  the  moon  passes  from  the 
south  side  to  the   north  side   of  the   ecliptic,  while  the 
opposite  node  is  called  the  descending  node. 

The  moon  at  the  end  of  the  month  never  comes  back  exactly  to 
the  point  of  beginning  among  the  stars,  on  account  of  'the  so-called 
"  perturbations "  of  her  orbit,  due  mostly  to  the  attraction  of  the 
sun.  One  of  the  most  important  of  these  perturbations  is  the 
"  regression  of  the  nodes."  These  slide  westward  on  the  ecliptic  just 
as  the  vernal  equinox  does  (precession),  but  much  faster,  completing 
their  circuit  in  about  nineteen  years  instead  of  26,000. 

135.  Interval  between  the  Moon's  Successive  Transits ; 
Daily  Retardation.  —  Owing  to  the    eastward   motion   of 
the  moon  among  the  stars  it  comes  to  the  meridian  about 
51    minutes   later    each    day,    on    the    average ;    but   the 


108  LESSONS  IN  ASTRONOMY 

retardation  ranges  all  the  way  from  38  minutes  to  66 
minutes,  on  account  of  the  variation  in  the  rate  of  the 
moon's  motion. 

The  average  retardation  of  the  moon's  rising  and  setting 
is  also  the  same  51  minutes ;  but  the  actual  retardation 
is  still  more  variable  than  that  of  the  meridian  transits, 
depending  to  some  extent  on  the  latitude  of  the  observer 
as  well  as  on  the  variations  in  the  moon's  motion. 

At  New  York  the  range  is  from  23  minutes  to  Ih17m ; 
that  is  to  say,  on  some  nights  the  rising  of  the  moon  is 
only  23  minutes  later  than  on  the  preceding  night,  while 
at  other  times  it  is  more  than  an  hour  and  a  quarter  behind- 
hand. In  high  latitudes  the  differences  are  still  greater. 
In  very  high  latitudes  the  moon,  when  it  has  its  greatest 
possible  declination,  becomes  circumpolar  for  a  certain  time 
each  month,  and  remains  visible  without  setting  at  all 
(like  the  midnight  sun)  for  a  greater  or  less  number  of 
days,  according  to  the  latitude  of  the  observer. 

There  is  always  one  day  in  the  month  on  which  the  moon  does 
not  rise,  and  another  on  which  it  does  not  set.  Why  ?  • 

136.  Harvest  and  Hunter's  Moon.  —  The  full  moon  that 
occurs  nearest  the  autumnal  equinox  is  called  the  "  harvest 
moon  " ;  the  one  next  following,  the  "  hunter's  moon."     At 
that  time  of  the  year  the  moon,  while  nearly  full,  rises  for 
several  consecutive  nights  almost  at  the  same  hour,  so  that 
the  moonlight  evenings  last  for  an  unusually  long  time. 
The  phenomenon,  however,  is  much  more  striking  in  north- 
ern Europe  and  in  Canada  than  in  the  United  States. 

137.  Form  of  the  Moon's  Orbit.  —  By  observation  of  the 
moon's  apparent  diameter  in  connection  with  observations 


FORM  OF  MOON'S  ORBIT  109 

of  her  place  in  the  sky,  we  can  determine  the  form  of  her 
orbit  around  the  earth  in  the  same  way  that  the  form  of 
the  earth's  orbit  around  the  sun  was  worked  out.  (See 
Appendix,  Sec.  428.)  The  moon's  apparent  diameter  ranges 
from  33'  33",  when  as  near  the  earth  as  possible,  to  29'  24", 
when  most  remote ;  and  her  orbit  turns  out  to  be  an  ellipse 
like  that  of  the  earth  around  the  sun,  but  of  much  greater 
eccentricity,  averaging  about  ^  (as  against  g1^).  We  say 
"  averaging  "  because  the  actual  eccentricity  is  variable  on 
account  of  perturbations. 

The  point  of  the  moon's  orbit  nearest  the  earth  is  called 
the  Perigee,  that  most  remote  the  Apogee,  and  the  indefi- 
nite line  passing  through  these  points  the  Line  of  Apsides, 
while  the  major  axis  is  that  portion  of  this  line  which  lies 
between  the  perigee  and  apogee.  This  line  of  apsides  is 
in  continual  motion  on  account  of  perturbations  (just  as 
the  line  of  nodes  is,  Sec.  134),  but  it  moves  eastward  instead 
of  westward,  completing  its  revolution  in  about  nine  years. 

In  her  revolution  about  the  earth  the  moon  observes  the 
same  law  of  equal  areas  that  the  earth  does  in  her  orbit 
around  the  sun  (Sec.  121). 

THE  MOON'S  DISTANCE 

138.  In  the  case  of  any  heavenly  body,  one  of  the  first 
and  most  fundamental  inquiries  relates  to  its  distance  from 
us ;  until  the  distance  has  been  measured  we  can  get  no 
knowledge  of  the  real  dimensions  of  its  orbit,  nor  of  the 
size,  mass,  etc.,  of  the  body  itself.  The  problem  is  usually 
solved  by  measuring  the  apparent  "  parallactic  "  displace- 
ment of  the  moon  as  seen  by  observers  at  widely  separated 


110  LESSONS  IN  ASTRONOMY 

stations.     Before  proceeding  -farther  we  must,  therefore, 
say  a  few  words  upon  the  subject  of  parallax. 

139.  Parallax.  —  In  general,  the  word  "  parallax  "  means 
the  difference  between  the  directions  of  a  heavenly  body 
as  seen  by  the  observer  and  as  seen  from  some  standard 
point  of  reference.     The  annual  or  heliocentric  parallax  of 
a  star  is  the  difference  of  the  star's  direction  as  seen  from 
the  earth  and  from  the  sun.     The  diurnal  or  geocentric 
parallax  of  the  sun,  the  moon,  or  a  planet  is  the  difference 
between  its  direction  as  seen  from  the  center  of  the  earth 
and  from  the  observer's  station  on  the  earth's  surface ;  or, 
what  comes  to  the  same  thing,  the  geocentric  parallax  is  the 
angle  at  the  body  made  by  two  lines  drawn  from  it,  one  to 
the  observer,  the  other  to  the  center  of  the  earth.     (Stars  have 
no  sensible  geocentric  parallax;   the  earth  as  seen  from 
them  is  a  mere  point.) 

In  Fig.  18  the  parallax  of  the  body  P,  for  an  observer 
at  0,  is  the  angle  OP C.  Obviously  this  diurnal  parallax 
is  zero  for  a  body  directly  overhead  at  Z,  and  is  the  greatest 
possible  for  a  body  on  the  horizon,  as  at  Ph. 

Moreover,  and  this  is  to  be  specially  noted,  this  parallax 
of  a  body  at  the  horizon  —  the  "  horizontal  parallax  "  —  is 
simply  the  angular  semi-diameter  of  the  earth  as  seen  from 
the  body.  When,  for  instance,  we  say  that  the  moon's  hori- 
zontal parallax  is  57',  it  is  equivalent  to  saying  that  seen 
from  the  moon  the  earth  appears  to  have  a  diameter  of  114'. 
In  the  same  way,  since  the  sun's  parallax  is  8". 8,  the 
diameter  of  the  earth  as  seen  from  the  sun  is  17 ".6. 

140.  Relation  between  Parallax  and  Distance When 

the  horizontal  parallax  of  any  heavenly  body  is  ascertained 
its  distance  follows  at  once  through  our  knowledge  of  the 


PARALLAX 


111 


earth's  dimensions.  If  we  know  how  large  a  ball  of  given 
size  appears,  we  can  tell  how  far  away  it  is ;  if  we  know 
how  large  the  earth  looks  from  the  moon,  we  can  find  the 
distance  between  them.  Thus,  when  in  the  triangle  CPhO 
(Fig.  18)  we  know  the  angle  at  PA,  and  the  side  CO,  the 
radius  of  the  earth,  we  can  compute  CPh  by  a  very  easy 
trigonometrical  calculation.  Evidently  the  more  remote 
the  body,  the  smaller  its 
parallax. 

Since  the  radius  of  the 
earth  varies  slightly  in  dif- 
ferent latitudes,  we  take  the 
equatorial  radius  as  a  stand- 
ard, and  the  equatorial  hori- 
zontal parallax  is  the  earth's 
equatorial  semi-diameter  as 
seen  from  the  body.  It  is 
this  which  is  usually  meant 
when  we  speak  simply  of 
"  the  parallax  "  of  the  moon,  of  the  sun,  or  of  a  planet 
without  adding  any  qualification,  but  never  when  we  speak 
of  the  parallax  of  a  star;  then  we  always  mean  the  annual 
parallax. 

141.  Parallax,  Distance,  and  Velocity  of  the  Moon.  - 
The  moon's  equatorial  horizontal  parallax  found  by  corre- 
sponding observations  made  at  different  parts  of  the  earth  is 
3422"  (57'  2")  according  to  Neison,  but  varies  considerably 
on  account  of  the  eccentricity  of  the  orbit.  From  this  paral- 
lax we  find  that  the  moon's  average  distance  from  the  earth 
is  about  60.3  times  the  earth's  equatorial  radius,  or  238,840 
miles,  with  an  uncertainty  of  perhaps  twenty  miles. 


FIG.  18.  —  Diurnal  Parallax 


112  LESSONS  IN  ASTRONOMY 

The  maximum  and  minimum  values  of  the  moon's  distance  are 
given.by  Nelson  as  252,972  and  221,617  miles.  It  will  be  noted  that 
the  average  distance  is  not  the  mean  of  the  two  extremes. 

Knowing  the  size  and  form  of  the  moon's  orbit,  the 
velocity  of  her  motion  is  easily  computed.  It  averages  a 
little  less  than  2300  miles  an  hour,  or  about  3350  feet  per 
second.  Her  mean  apparent  angular  velocity  among  the 
stars  is  about  33',  which  is  just  a  little  greater  than  the 
apparent  diameter  of  the  moon  itself. 

142.  Diameter,  Area,  and  Bulk  of  the  Moon.  —  The  mean 
apparent  diameter  of  the  moon  is  31'  7".     Knowing  its 
distance,  its  real  diameter  comes  out  2163  miles.     This 
is  0.273  of  the  earth's  diameter. 

Since  the  surfaces  of  globes  vary  as  the  squares  of  their 
diameters,  and  their  volumes  as  the  cubes,  this  makes 
the  surface  area  of  the  moon  equal  to  about  -fa  of  the 
earth's,  and  the  volume  (or  bulk)  almost  exactly  ^  of 
the  earth's. 

No  other  satellite  is  nearly  as  large  as  the  moon  in  comparison 
with  its  primary  planet.  The  earth  and  moon  together,  as  seen  from 
a  distance,  are  really  in  many  respects  more  like  a  double  planet  than 
like  a  planet  and  satellite  of  ordinary  proportions.  At  a  time,  for 
instance,  when  Venus  happens  to  be  nearest  the  earth  (at  a  distance 
of  about  25,000000  miles)  her  inhabitants  (if  she  has  any)  would 
see  the  earth  just  about  as  brilliant  as  Venus  herself  at  her  best 
appears  to  us,  and  the  moon  would  be  about  as  bright  as  Sirius, 
oscillating  backwards  and  forwards  about  £°  each  side  of  the  earth, 
once  a  month. 

143.  Mass,  Density,  and  Superficial  Gravity  of  the  Moon. 
—  Her  mass  is  about  ^  of  the  earth's  mass  (0.0125).     The 
actual  measurement  of  the  moon's  mass  is  an  extremely 


THE  MOON'S  ROTATION  113 

difficult  problem,  and  the  methods  pursued  are  quite  beyond 

JY/T  o  co 

the  scope  of  this  book.     Since  the  density  is  equal  to  ^—, , 

the  density  of  the  moon  as  compared  to  that  of  the  earth 
is  found  'to  be  0.613,  or  about  3.4  the  density  of  water 
(the  earth's  density  being  5.58).  This  is  a  little  above 
the  average  density  of  the  rocks  which  compose  the  crust 
of  the  earth. 

The  "  superficial  gravity,"  or  the  attraction  of  the  moon 
for  bodies  at  its  surface,  is  only  about  one-sixth  that  at  the 
surface  of  the  earth.     This  is  a  fact  that 
must  be  borne  in  mind  in  connection      JL 
with  the  enormous  scale  of  the  craters  on    I  ! . : 
the  moon.     Volcanic  forces  there  would 
throw  materials  to  a  vastly  greater  dis- 
tance than  on  the  earth. 

144,    Rotation   of    the    Moon.  —  The 
moon  turns  on  its  axis  once  a  month,  in 
exactly  the  time  occupied  by  its  revo- 
lution around  the  earth;  its   day  and 
night  are,  therefore,  each  about  a  fortnight  in  length,  and 
in  the  long  run  it  keeps  the  same  side  always  toward  the 
earth.     We  see  to-day  precisely  the  same  face  of  the  moon 
which  Galileo  did  when  he  first  looked  at  it  with  his  tele- 
scope.    The  opposite  face  has  never  been  seen  from  the 
earth,  and  probably  never  will  be. 

It  is  difficult  for  some  to  see  why  a  motion  of  this  sort  should 
be  considered  a  rotation  of  the  moon,  since  it  closely  resembles  the 
motion  of  a  ball  carried  on  a  revolving  crank  (Fig.  19).  Such  a 
ball,  they  say,  "  revolves  around  the  shaft,  but  does  not  rotate  on  its 
own  axis."  It  does  rotate,  however ;  for  if  we  mark  one  side  of  the 


114  LESSONS  IN  ASTRONOMY 

ball,  we  shall  find  the  marked  side  presented  successively  to  every 
point  of  the  compass  as  the  crank  turns  around,  so  that  the  ball 
turns  on  its  own  axis  as  really  as  if  it  were  whirling  upon  a  pin 
fastened  to  the  table.  By  virtue  of  its  connection  with  the  crank, 
the  ball  has  two  distinct  motions:  (1)  the  motion  of  translation, 
which  carries  its  center  in  a  circle  around  the  shaft;  (2)  an  addi- 
tional motion  of  rotation  around  a  line  drawn  through  its  center  of 
gravity  parallel  to  the  shaft. 

Rotation  consists  essentially  in  this :  A  line  connecting  any  two 
points  in  the  rotating  body,  and  produced  to  the  celestial  sphere,  will 
sweep  out  a  circle  upon  it.  In  every  rotating  body  one  line,  however, 
can  be  drawn  through  the  center  of  the  body,  so  that  the  circle 
described  by  it  in  the  sky  will  be  infinitely  small.  This  is  the  axis 
of  the  body. 

145.  Librations.  —  The  behavior  of  the  moon,  however,  differs 
essentially  from  that  of  the  ball  on  the  crank,  showing  that  her  rota- 
tion and  orbital  revolution  are  really  independent,  though  identical 
in  period.     While  in  the  long  run  the  moon  keeps  the  same  face 
towards  the  earth,  it  is  not  so  from  day  to  day.     With  reference  to 
the  center  of  the  earth,  -it  is  continually  oscillating  a  little,  and 
these  oscillations  constitute  what  are  called  Librations,  of  which  \ve 
distinguish  three :  (1) -the  libration  in  latitude,  by  which  the  north 
and  south  poles  are  alternately  presented  to  the  earth ;    (2)   the 
libration  in  longitude,  by"  which  the  east  and  west  sides  of  the  moon 
are  alternately  tipped  a  little  towards  us ;  and  (3)  the  diurnal  libra- 
tion, which  enables  us  to  look  over  whatever  edge  of  the  moon  is 
uppermost  when  it  is  near  the  horizon.     Owing  to  these  librations, 
we  see  considerably  more  than  half  of  the  moon's  surface  at  one  time 
and  another.     About  4V  per  cent  of  it  is  always  visible ;  41  per  cent 
never  visible ;  and  a  belt  at  the  edge  of  the  moon,  covering  about 
18  per  cent,  is  rendered  alternately  visible  and  invisible  by  libration. 
The  explanation  of  the  peculiarity  of  the  moon's  rotation  is  to  be 
found  in  the  theory  of  "  tidal  evolution."     (See  Manual  of  Astronomy, 
Sec.  346.) 

146.  Phases  of  the  Moon.  —  Since  the  moon  is  an  opaque 
globe  shining  merely  by  reflected  light,  we  can  see  only 


THE  MOON'S  PHASES 


115 


that  hemisphere  of  her  surface  on  which  the  sun  is  shining, 
and  of  the  illuminated  hemisphere  only  that  portion  which 
happens  to  be  turned  towards  the  earth. 

When  the  moon  is  between  the  earth  and  the  sun  (new 
moon)  the  side  presented  to  us  is  dark,  and  the  moon  is 


FIG.  20.  —  The  Moon's  Phases 


then  invisible.  A  week  later,  at  the  end  of  the  first  quarter, 
half  of  the  illuminated  hemisphere  is  visible,  and  we  have 
the  half-moon,  as  we  also  do  a  week  after  the  full.  Between 
the  new  moon  and  the  half-moon,  during  the  first  and  last 


116  LESSONS  IN  ASTRONOMY 

quarters  of  the  lunation,  we  see  less  than  half  of  the 
illuminated  portion,  and  then  have  the  "  crescent "  phase. 
Between  half-moon  and  the  full  moon,  during  the  second 
and  third  quarters  of  the  lunation,  we  see  more  than  half 
of  the  moon's  illuminated  side,  and  we  have  then  what  is 
called  the  "  gibbous  "  phase. 

Fig.  20  (in  which  the  light  is  supposed  to  come  from  a  point  far 
above  the  circle  which  represents  the  moon's  orbit)  shows  the  way  in 
which  the  phases  are  distributed  through  the  month. 

The  line  which  separates  the  dark  portion  of  the  disk 
from  the  bright  is  called  the  Terminator,  and  is  always  a 
semi-ellipse,  since  it  is  a  semicircle  viewed  obliquely,  as 
shown  by  Fig.  21,  A.  Draftsmen  sometimes  incorrectly 
represent  the  crescent  form  by  a  construction  like  Fig.  21,  B, 
in  which  a  smaller  circle  has  a  por- 
tion cut  out  of  it  by  an  arc  of  a 
larger  one.  It  is  to  be  noticed  also 
that  ab,  the  line  which  joins  the 
"cusps,"  or  points,  of  the  crescent, 
is  always  perpendicular  to  a  line 
drawn  from  the  moon  to  the  sun,  so 
that  tlip  %rw-g  "<rp  "^"nys  titrnfl  j-!ra*fiy  ninny  f^^  fflf  <?*/« 
The  precise  position  in  which  they  will  stand  at  any  time 
is,  therefore,  perfectly  predictable  and  has  nothing  whatever 
to  do  with  the  weather.  (Pupils  have  probably  heard  of 
the  "  wet  moon  "  and  "  dry  moon  "  superstition.) 

147.    Earth-Shine  on  the  Moon Near  the  time  of  new 

moon  the  portion  of  the  moon's  disk  which  does  not  get 
the  sunlight  is  easily  visible,  illuminated  by  a  pale  reddish 
light.  This  light  is  earth-shine,  —  the  earth  as  seen  from 
the  moon  being  then  nearly  "  full."  The  red  color  is  due  to 


THE  MOON'S  PHYSICAL  CHARACTERISTICS      117 

the  fact  that  the  light  sent  to  the  moon  from  the  earth  has 
passed  twice  through  our  atmosphere,  and  so  has  acquired 
the  sunset  tinge.  Seen  from  the  moon,  the  earth  would 
be  itself  a  magnificent  moon  about  2°  in  diameter,  showing 
the  same  phases  as  the  moon  does  to  us. 

Taking  everything  into  account,  the  earth-shine  is  probably  fifteen 
to  twenty  times  as  strong  as  the  light  of  the  moon  at  similar  phases. 
Since  the  moon  keeps  always  the  same  face  towards  the  earth,  the 
earth  is  visible  only  from  that  part  of  the  moon  which  faces  us,  and 
remains  nearly  stationary  in  the  lunar  sky,  neither  rising  nor  setting. 
It  is  easy  to  see  that  she  would  be  a  very  beautiful  object,  on  account 
of  the  changes  which  would  be  continually  going  on  upon  her  surface 
due  to  snow,  storms,  clouds,  growth  of  vegetation,  etc. 

PHYSICAL   CHARACTERISTICS   OF   THE   MOON 

148.  Absence  of  Air  and  Water.  —  The  moon's  atmos- 
phere, if  there  is  any,  is  extremely  rare,  its  density  at  the 
moon's  surface  being  probably  not  more  than  y^  part  of 
that  of  our  own  atmosphere. 

The  evidence  on  the  point  is  twofold  :  First,  the  telescopic  appear- 
ance. There  is  no  haze,  shadows  are  perfectly  black;  there  is  no 
sensible  twilight  at  the  points  of  the  crescent,  and  all  outlines  are 
visible  sharply  and  without  the  least  blurring  such  as  would  be  due 
to  the  intervention  of  an  atmosphere.  Second,  the  absence  of  refrac- 
tion when  the  moon  intervenes  between  us  and  any  distant  body. 
When  the  moon  "  occults  "  a  star,  for  instance,  there  is  no  distortion 
or  discoloration  of  the  star -disk,  but  both  the  disappearance  and  the 
reappearance  are  practically  instantaneous. 

Of  course  if  there  is  no  air,  there  can  be  no  liquid  water, 
since  the  water  would  immediately  evaporate  and  form  an 
atmosphere  of  vapor  if  air  were  not  present.  It  is  not  impos- 
sible, however,  nor  perhaps  improbable,  that  solid  water  (ice 


118  LESSONS  IN  ASTRONOMY 

and  snow)  may  exist  on  the  moon's  surface.  Although  ice 
and  snow  liberate  a  certain  amount  of  vapor,  yet  at  a  low 
temperature  the  quantity  would  be  insufficient  to  make  an 
atmosphere  dense  enough  to  be  observed  from  the  earth. 

If  the  moon  once  formed  a  portion  of  the  earth,  as  is  likely,  the 
absence  of  air  and  water  requires  explanation,  and  there  have  been 
many  interesting  speculations  on  the  subject  into  which  we  cannot 
enter.  (The  student  is  referred  to  the  Manual  of  Astronomy, 
Sec.  209.) 

149.  The  Moon's  Light.  —  In  its  quality  moonlight  is 
simply  sunlight,  showing  a  spectrum  identical  in  every 
detail  with  that  of  the  light  coming  from  the  sun  itself, 
except  as  the  intensity  of  different  portions  of  the  spectrum 
is  slightly  altered  by  its  reflection  from  the  lunar  surface. 

The  brightness  of  full  moonlight  as  compared  with  sun- 
light is  about  one  six-hundred-thousandth.  According  to 
this,  if  the  whole  visible  hemisphere  were  packed  with  full 
moons,  we  should  receive  from  it  only  about  one-eighth  of 
the  light  of  the  sun. 

The  half-moon  does  not  give  nearly  half  as  much  light 
as  the  full  moon.  Near  the  full  the  brightness  is  suddenly 
and  greatly  increased,  probably  because  at  any  time  except 
the  full  the  moon's  visible  surface  is  more  or  less  darkened 
by  shadows  which  disappear  at  the  moment  of  full. 

The  average  "  albedo,"  or  reflecting  power,  of  the  moons 
surface  is  given  by  Zollner  as  0.174 ;  i.e.,  the  moon's  sur- 
face reflects  a  little  more  than  one-sixth  of  the  light  that 
falls  upon  it.  There  are,  however,  great  differences  in  the 
brightness  of  the  different  portions  of  the  moon's  surface. 
Some  spots  are  nearly  as  white  as  snow  or  salt,  and  others 
as  dark  as  slate. 


THE  MOON'S  HEAT  119 

150.  Heat  of  the  Moon.  —  For  a  long  time  it  was  impos- 
sible to  detect  the  moon's  heat  by  observation.  Even  when 
concentrated  by  a  large  lens,  it  is  too  feeble  to  be  shown 
by  the  most  delicate  thermometer.  With  modern  appa- 
ratus, however,  it  is  easy  enough  to  perceive  the  heat  of 
lunar  radiation,  though  the  measurement  is  extremely  diffi- 
cult. The  total  amount  of  heat  sent  by  the  full  moon  to 
the  earth  appears  to  be  about  yy-oVFo  °^  *na^  sen^  ^7  the 
sun ;  i.e.,  the  full  moon  in  two  days  sends  us  about  as  much 
heat  as  the  sun  does  in  one  second.  But  the  results  of 
different  observers  differ  rather  widely. 

A  considerable  portion  of  the  lunar  heat  seems  to  be 
simply  reflected  from  the  surface  like  light,  while  the  rest, 
perhaps  three-fourths  of  the  whole,  is  "  obscure  heat,"  i.e.^ 
heat  which  has  first  been  absorbed  by  the  moon's  surface 
and  then  radiated,  like  the  heat  from  a  brick  that  has  been 
warmed  by  the  sunshine. 

As  to  the  temperature  of  the  moon's  surface,  it  is  impos- 
sible to  be  very  certain.  During  the  long  lunar  night  of 
fourteen  days  the  temperature  must  inevitably  fall  appall- 
ingly low,  —  perhaps  200°  or  300°  below  zero.  On  the 
other  hand,  the  lunar  rocks  are  exposed  to  the  sun's  rays 
in  a  cloudless  sky  for  fourteen  days  at  a  time,  so  that  if 
they  were  protected  by  air,  like  the  rocks  upon  the  earth, 
they  would  certainly  become  intensely  heated.  The  recent 
observations  of  Very,  which  are  apparently  conclusive, 
seem  to  show  that  on  all  the  dark  portion  of  the  moon, 
and  near  its  boundary  on  the  illuminated  portion  even,  the 
temperature  is  far  below  zero,  and  may  fall  as  low  as  that 
of  liquid  air ;  but  that  in  the  equatorial  regions  the  temper- 
ature a  few  hours  after  "noon"  rises  very  high,  probably 


120  LESSONS  IN  ASTRONOMY 

above  that  of  boiling  water,  thus  confirming  Lord  Rosse's 
conclusion  of  more  than  thirty  years  ago.  But  the  mean 
temperature  of  even  the  equatorial  regions  is  probably 
everywhere  below  the  freezing  point  of  water. 

151.  Lunar  Influences  on  the  Earth.  —  The  most  impor- 
tant effect  produced  upon  the  earth  by  the  moon  is  the 
generation  of  the  tides  in  cooperation  with  the  sun.     There 
are  also  certain  well-ascertained  disturbances  of  the  terres- 
trial magnetism  connected  with  the  approach  and  recession 
of  the  moon  in  its  oval  orbit ;  and  this  ends  the  chapter  of 
proved  lunar  influences. 

The  multitude  of  current  beliefs  as  to  the  controlling 
influence  of  the  moon's  phases  and  changes  upon  the  weather 
and  the  various  conditions  of  life  are  mostly  unfounded. 
It  is  quite  certain  that  if  the  moon  has  any  influence  at  all 
of  the  sort  imagined,  it  is  extremely  slight,  —  so  slight  that 
it  has  not  yet  been  demonstrated,  though  numerous  inves- 
tigations have  been  made  expressly  for  the  purpose  of 
detecting  it.  Different  workers  continually  come  to  con- 
tradictory results. 

152.  The  Moon's  Telescopic  Appearance.  —  Even  to  the 
naked  eye  the  moon  is  a  beautiful  object,  diversified  with 
curious  markings  connected  with  numerous  popular  legends. 
In  a  powerful  telescope  these  naked-eye  markings  vanish, 
and  are  replaced  by  a  multitude  of  smaller  details  which 
make  the  moon,  on  the  whole,  the  most  interesting  of  all 
telescopic  objects  —  especially  to  instruments  of  moderate 
size,  say  from  six  to  ten  inches  in  diameter,  which  gener- 
ally give  a  more  pleasing  view  than  instruments  either 
much  larger  or  much  smaller.     An  instrument  of  this  size, 
with  magnifying  powers  between  250  and  500,  virtually 


THE  MOON'S  SURFACE  STRUCTURE 


121 


brings  the  moon  within  a  distance  ranging  from  1000  to 
500  miles.  Any  object  half  a  mile  in  diameter  on  the 
moon  is  distinctly  visible.  A  long  line  or  streak  even  less 
than  a  quarter  of  a  mile  across  can  easily  be  seen. 

For  most  purposes  the  best  time  to  look  at  the  moon  is  when  it  is 
between  six  and  ten  days  old ;  at  the  time  of  full  moon  few  parts  of  the 
surface  are  well  seen.  It  is  evident  that  while  with  the  telescope  we 
should  be  able  to  see  such  objects  as  lakes,  rivers,  forests,  and  great  cit- 
ies, if  they  existed  on  the  moon,  it  would  be  hopeless  to  expect  to  distin- 
guish any  of  the  minor  indications  of  life,  such  as  buildings  or  roads. 

153.  The  Moon's  Surface  Structure.  —  The  moon's  sur- 
face for  the  most  part  is  extremely  broken.  The  earth's 
mountains  are 
mainly  in  long 
ranges,  like  the 
Andes  and  Hima- 
layas. On  the 
moon  the  ranges 
are  few  in  num- 
ber; but,  on  the 
other  hand,  the 
surface  is  pitted 
all  over  with  great 
craters,  which 
resemble  very 

closely  the  volcanic  craters  on  the  earth's  surface,  though 
on  an  immensely  greater  scale.  The  largest  terrestrial 
craters  do  not  exceed  six  or  seven  miles  in  diameter;  many 
of  those  on  the  moon  are  fifty  or  sixty  miles  across,  and 
some  more  than  a  hundred,  while  scores  are  from  five  to 
twenty  miles  in  diameter. 


FIG.  22.  —  Normal  Lunar  Crater 


122 


LESSONS  IN  ASTROXOMY 


The  normal  lunar  crater  (Fig.  22)  is  nearly  circular,  sur- 
rounded by  a  mountain  ring,  which  rises  anywhere  from 
1000  to  20,000  feet  above  the  neighboring  country.  The 
floor  within  the  ring  may  be  either  above  or  below  the  out- 
side level ;  some  craters  are  deep,  and  some  are  filled 
nearly  to  the  brim.  Frequently  in  the  center  of  the 
crater  there  rises  a  group  of  peaks  which  attain  the  same 

elevation  as  the 
encircling  ring,  and 
these  central  peaks 
often  show  holes  or 
minute  craters  in 
their  summits. 

On  some  portions 
of   the  moon    these 
craters    stand    very 
thickly.     This  is  es- 
pecially the  case  near 
the  moon's  south 
pole.  It  is  noticeable, 
also,  that  as  on  the 
earth   the  youngest 
mountains  are  gen- 
erally the  highest,  so 
on  the  moon  the  most 
recent  craters  are  generally  deepest  and  most  precipitous. 
The  height  of  a  lunar  mountain  can  be  measured  with 
notable  accuracy  by  means  of  its  shadow. 

The  striking  resemblance  of  these  lunar  craters  to  terrestrial 
"volcanoes  makes  it  natural  to  assume  that  they  have  a  similar 
origin.  This,  however,  is  not  quite  certain,  for  there  are  notable 


FIG.  23.  —  Gassendi 


LUNAR  FORMATIONS 


128 


difficulties  in  the  way  of  the  volcanic  theory,  especially  in  the  case  of 
what  are  called  the  great  "Bulwark  Plains,"  so  extensive  that  a, 
person  standing  in  the  center  could  not  even  see  the  summit  of  the 
surrounding  ring  at  any  point ;  and  yet  there  is  no  line  of  distinction 
between  them  and  the  smaller  craters,  —  the  series  is  continuous. 
Moreover,  on  the  earth  volcanoes  necessarily  require  the  action  of 
air  and  water,  which  do  not  now  exist  on  the  moon  ;  so  that  if  these 
lunar  craters  are  really 
the  result  of  volcanic 
eruptions,  they  must  be 
ancient  formations,  for 
there  is  no  satisfactory 
evidence  of  any  present 
volcanic  activity.  Fig.  23 
represents  one  of  the 
finest  lunar  craters,  Gas- 
sendi,  about  fifty-six 
miles  in  diameter,  which 
is  best  seen  about  three 
days  after  the  half- 
moon. 

154.  Other  Lunar 
Formations.  —  The 
craters  and  mount- 
ains are  not  the  only 
interesting  features 
on  the  moon's  sur- 
face. There  are  many 
which  go  by  the  name  of  "  rills,"  and  may  once  have  been 
watercourses.  (See  Fig.  24.)  Then  there  are  many  straight 
"  clefts  "  half  a  mile  or  so  wide,  and  of  unknown  depth,, 
running  in  some  cases  several  hundred  miles  straight 
through  mountain  and  valley,  without  any  apparent  regard 
to  the  accidents  of  the  surface. 


FIG.  24.  —  Copernicus 

deep,    narrow,    crooked  valleys- 


124  LESSONS  IN  ASTRONOMY 

Most  curious  of  all  are  the  light-colored  streaks,  or 
"  rays,"  which  radiate  from  certain  of  the  craters,  extend- 
ing in  some  cases  a  distance  of  many  hundred  miles. 
They  are  usually  from  five  to  ten  miles  wide,  and  neither 
elevated  nor  depressed  to  any  considerable  extent  with 
reference  to  the  general  surface.  Like  the  clefts,  they 
pass  across  valley  and  mountain,  and  sometimes  straight 
through  craters,  without  any  change  in  width  or  color. 
No  satisfactory  explanation  of  them  has  yet  been  given. 
The  most  remarkable  of  these  "  ray-systems  "  is  the  one 
connected  with  the  great  crater  Tycho,  not  very  far  from 
the  moon's  south  pole.  The  rays  are  not  very  conspicuous 
until  within  a  few  days  of  full  moon,  but  at  that  time  they, 
and  the  crater  from  which  they  diverge,  constitute  by  far 
the  most  striking  feature  of  the  telescopic  view. 

155.  Changes  on  the  Moon.  —  It  is  certain  that  there 
are  no  conspicuous  changes  on  the  moon's  surface ;  no  such 
transformations  as  would  be  presented  by  the  earth  viewed 
with  a  telescope  from  the  moon,  —  no  clouds,  no  storms, 
no  snow  of  winter,  and  no  spread  of  verdure  in  the  spring. 
At  the  same  time  it  is  confidently  maintained  by  some 
observers  that  here  and  there  perceptible  alterations  do 
take  place  in  the  details  of  the  lunar  surface.  Professor 
W.  H.  Pickering,  the  younger  brother  of  the  Director  of 
the  Harvard  Observatory,  is  at  present  the  most  prominent 
supporter  of  this  view. 

The  difficulty  in  settling  the  question  arises  from  the 
great  changes  which  take  place  in  the  appearance  of  a 
lunar  object,  according  to  the  angle  at  which  the  sunlight 
strikes  it.  Other  conditions  also,  such  as  the  height  of  the 
moon  above  the  horizon  and  the  clearness  and  steadiness 


LUNAR  MAPS  AND  NOMENCLATURE      125 

of  the  air,  affect  the  appearance ;  and  it  is  very  difficult  to 
secure  a  sufficient  identity  of  conditions  at  different  times 
of  observation  to  be  sure  that  apparent  changes  are  real. 
It  is  probable  that  the  question  will  finally  be  settled  by 
photography.  (For  further  discussion  of  this  subject,  see 
General  Astronomy,  Art.  272.) 

156.  Lunar  Maps  and  Nomenclature.  —  A  number  of 
maps  of  the  moon  have  been  constructed  by  different 
observers.  The  most  recent  and  extensive  is  that  by 
Schmidt  of  Athens,  on  a  scale  of  seven  feet  in  diameter ; 
it  was  published  by  the  Prussian  government  in  1878. 
Perhaps  the  best  for  ordinary  observers  is  that  given  in 
Webb's  "  Celestial  Objects  for  Common  Telescopes."  We 
present  here  (Fig.  25)  a  skeleton  map,  which  indicates  the 
position  of  about  fifty  of  the  leading  objects. 

As  for  the  names  of  the  lunar  objects,  the  great  plains 
upon  the  surface  were  called  by  Galileo  "  oceans,"  or  "  seas" 
(Maria),  because  he  supposed  that  these  grayish  surfaces, 
which  are  visible  to  the  naked  eye  and  conspicuous  in  a 
small  telescope,  though  not  with  a  large  one,  were  covered 
with  water.  Thus  we  have  the  "  Oceanus  Procellarum  " 
(Sea  of  Storms)  and  "  Mare  Imbrium "  (Sea  of  Showers). 
The  ten  mountain  ranges  on  the  moon  are  mostly  named 
for  terrestrial  mountains,  as  Caucasus,  Alps,  Apennines, 
though  two  or  three  bear  the  names  of  astronomers,  like 
Leibnitz,  Doerfel,  etc.  The  conspicuous  craters  bear  the 
names  of  ancient  and  medieval  astronomers  and  philoso- 
phers, as  Plato,  Archimedes,  Tycho,  Copernicus,  Kepler, 
and  Gassendi.  This  system  of  nomenclature  seems  to 
have  originated  with  Riccioli,  who  made  one  of  the  first 
maps  of  the  moon  in  1650. 


126 


LESSONS  IN  ASTRONOMY 


156*.  Lunar  Photography.  —  The  earliest  success  in  lunar 
photography  was  that  of  W.  C.  Bond  at  Cambridge  (U.S.) 
in  1850,  using  the  old  daguerreotype  process.  This  was 


FIG.  25.  —  Map  of  the  Moon,  reduced  from  Nelson 

soon  followed  by  the  work  of  De  la  Rue  in  England,  and  a 
little  later  by  Dr.  Henry  Draper  and  Lewis  M.  Rutherfurd 
in  New  York.  Until  very  lately  Mr.  Rutherfurd's  pictures 
remained  unrivaled ;  but  since  1890  there  has  been  a  great 


LUNAR  PHOTOGRAPHY 


127 


advance.  At  various  places,  especially  at  Cambridge  and 
the  Lick  and  Yerkes  observatories  in  this  country,  and  at 
Paris,  most  admirable  photographs  have  been  made  which 
bear  enlargement  well,  and  show  details  almost  (not  quite) 
as  perfectly  as  they  can  be  seen  with  the  telescope. 
Already  maps  of  the  lunar  surface  have  been  made  from 
them  exceeding  in  accuracy  even  the  great  map  of  Schmidt 
mentioned  in  the  preceding  article. 


KEY  TO  THE  PRINCIPAL  OBJECTS  INDICATED  IN  FIG.  25 


A.    Mare  Humorum. 
B.    Mare  Nectaris. 
C.    Oceanus  Procellarum. 
D.    Mare  Fecunditatis. 
E.    Mare  Tranquillitatis. 
F.    Mare  Crisium. 
G.    Mare  Serenitatis. 

K  .   Mare  Nubium. 
L.    Mare  Frigoris. 
T.    Leibnitz  Mountains. 
U.    Doerfel  Mountains. 
V.    Rook  Mountains. 
W.    D'Alembert  Mountains. 
X.    Apennines. 

H.   Mare  Imbrium. 

Y.    Caucasus. 

7.    Sinus  Iridum. 

Z.    Alps. 

1. 

Clavius. 

14. 

Alphonsus. 

27. 

Eratosthenes. 

2. 

Schiller. 

15. 

Theophilus. 

28. 

'Proclus. 

3. 

Maginus. 

16. 

Ptolemy. 

28'. 

Pliny. 

4. 

Schickard. 

17. 

Langrenus. 

29. 

Aristarchus. 

5. 

Tycho. 

18. 

Hipparchus. 

30. 

Herodotus. 

6. 

Walther. 

19. 

Grimaldi. 

31. 

Archimedes. 

7. 

Purbach. 

20. 

Flarnsteed. 

32. 

Cleomedes. 

8. 

Petavius. 

21. 

Messier. 

33. 

Aristillus. 

9. 

"  The  Railway." 

22. 

Maskelyne. 

34. 

Eudoxus. 

10. 

Arzachel. 

23. 

Triesnecker. 

35. 

Plato. 

11. 

Gassendi. 

24. 

Kepler. 

36. 

Aristotle. 

12. 

Catherina. 

25. 

Copernicus. 

37. 

Endymion. 

13. 

Cyrillus. 

26. 

Stadius. 

128  LESSONS  IN  ASTRONOMY 

The  half-tone  engraving  which  forms  the  frontispiece  is  from  two 
photographs,  the  first  of  which,  of  the  moon  a  little  past  the  full, 
was  made  by  Professor  Hale  in  1892  at  his  Kenwood  Observatory  in 
Chicago  ;  the  other  is  enlarged  from  a  magnificent  photograph  made 
by  Ritchey  with  the  non-photographic  forty-inch  telescope  of  the 
Yerkes  Observatory,  a  yellowish  color-screen  being  interposed  in 
front  of  the  sensitive  plate  to  cut  off  the  red,  violet,  and  ultra-violet 
rays  in  accordance  with  a  suggestion  by  Professor  Hale.  The 
original  negative,  about  six  inches  in  diameter,  is  certainly  unsur- 
passed by  any  hitherto  made  with  photographic  lenses  or  reflectors. 
The  portion  shown  includes  the  great  crater  Theophilus,  60  miles 
in  diameter  and  17,000  feet  deep,  with  its  neighbors  Cyrillus  and 
Catherina. 

The  reader  will  notice  the  relative  ages  of  the  craters.  On 
the  moon  the  deepest  craters  and  the  highest  mountains  are  the 
youngest,  as  is  the  case  with  the  mountains  on  the  earth.  The 
Himalayas,  the  Alps,  and  the  Andes  are  infants  compared  with 
the  Laurentian  range,  now  low  because  worn  down  by  time. 


CHAPTER  VI 

THE  SUN  AND  SPECTROSCOPE 

Its  Distance,  Dimensions,  Mass,  and  Density  —  Its  Rotation,  Surface,  and 
Spots  —  The  Spectroscope  and  the  Chemical  Constitution  of  the  Sun  — 
The  Chromosphere  and  Prominences  —  The  Corona  —  The  Sun's  Light  — 
Measurement  and  Intensity  of  the  Sun's  Heat  —  Theory  of  its  Maintenance 
and  Speculations  regarding  the  Age  of  the  Sun 

157.  The  sun  is  a  star,  the  nearest  of  them  —  a  hot, 
self-luminous  globe,  enormous  as  compared  with  the  earth 
and  moon,  though  probably  only  of  medium  size  as  a  star ; 
but  to  the  earth  and  the  other  planets  which  circle  around 
it,  it  is  the  grandest  and  most  important  of  all  the  heav- 
enly bodies.     Its  attraction  controls  their  motions,  and  its 
rays  supply  the   energy  which  maintains  every  form  of 
activity  upon  their  surfaces. 

158.  The  Sun's  Distance.  —  The  mean  distance  of  the 
sun  from  the  earth  (the  astronomical  unit  of  distance)  is  a 
little  less  than  93,000,000  miles.     There  are  many  methods 
of  determining  it,  some  of  which  depend  on  a  knowledge  of 
the  Velocity  of  Light  (Appendix,  Sees.  434  and  436),  while 
others  depend  on  finding  the  sun's  horizontal  parallax. 
(For  a  resumS  of   the  subject,   see   General  Astronomy, 
Chap.  XIV,  or  Chap.  XV  of  the  Manual  of  Astronomy.) 
The  mean  value  of  this  parallax  is  very  nearly  8". 8.     In 
other  words,   as    seen   from   the    sun,   the   earth  has  an 
apparent  diameter  of  about  17".6  (Sec.  139).     The   dis- 
tance is  variable,  to  the  extent  of  about  1,500000  miles, 

129 


130  LESSONS  IN  ASTRONOMY 

on  account  of  the  eccentricity  of  the  earth's  orbit,  the 
earth  being  almost  3,000000  miles  nearer  to  the  sun  on 
December  31  than  on  July  1. 

Knowing  the  distance  of  the  earth  from  the  sun,  the 
earth's  orbital  velocity  follows  at  once  by  dividing  the  cir- 
cumference of  the  orbit  by  the  number  of  seconds  in  a 
year.  It  comes  out  18.5  miles  per  second.  (Compare  this 
with  the  velocity  of  a  cannon-ball,  which  seldom  exceeds 
2500  feet  per  second.)  In  traveling  this  18?  miles,  the 
deflection  of  the  earth's  motion  from  a  perfectly  straight  line 
amounts  to  less  than  one-ninth  of  an  inch. 

159.  The  distance  of  the  sun  is  of  course  enormous  compared 
with  any  distance  upon  the  earth's  surface.     Perhaps  the  simplest 
illustration  which  will  give  us  any  conception  of  it  is  that  drawn 
from  the  motion  of  a  railway  train,  which,  going  a  thousand  miles 
a  day  (nearly  forty-two  miles  an  hour  without  stops)  would  take 
254^  years  to  make  the  journey.    If  sound  were  transmitted  through 
interplanetary  space,  and  at  the  same  rate  as  in  our  own  air.  it  would 
make  the  passage  in  about  fourteen  years ;  i.e.,  an  explosion  on  the 
sun  would  be  heard  by  us  fourteen  years  after  it  actually  occurred. 
Light  traverses  the  distance  in  499  seconds. 

160.  Dimensions  of  the  Sun.  —  The  sun's  mean  apparent 
diameter  is  33'  4".     Since  at  its  mean  distance  1"  equals 
450.36  miles,  its  diameter  is  866,500  miles,  or  109£  times 
that  of  the  earth.     If  we  suppose  the  sun  to  be  hollowed 
out,  and  the  earth  placed  at  the  center  of  it,  the  sun's 
surface  would  be  433,000  miles  away.     Now,  since  the 
distance  of  the  moon  from  the  earth  is  about  239,000  miles, 
she  would  be  only  a  little  more  than  half-way  out  from 
the  earth  to  the  inner  surface  of  the  hollow  globe,  which 
would  thus  form  a  very  good  background  for  the  study  of 
the  lunar  motions. 


THE  SUN'S  DIMENSIONS,  MASS,  AND  DENSITY     131 

If  we  represent  the  sun  by  a  globe  two  feet  in  diameter,  the  earth 
on  the  same  scale  would  be  0.22  of  an  inch  in  diameter,  the  size  of 
a  very  small  pea.  Its  distance  from  the  sun  would  be  just  about 
220  feet,  and  the  nearest  star,  still  on  the  same  scale,  would  be  8000 
miles  away,  on  the  other  side  of  the  earth. 

Since  the  surfaces  of  globes  are  proportional  to  the 
squares  of  their  radii,  the  surface  of  the  sun  exceeds 
that  of  the  earth  in  the  ratio  of  (109. 5)2:  1;  i.e.,  the 
area  of  its  surface  is  about  12,000  times  the  surface  of 
the  earth. 

The  volumes  of  spheres  are  proportional  to  the  cubes  of 
their  radii ;  hence  the  sun's  volume,  or  bulk,  is  (109.5)3,  or 
1,300000  times  that  of  the  earth. 

161.  The  Sun's  Mass,  Density,  and  Superficial  Gravity.  — 
The  mass  of  the  sun  is  about  332,000  times  that  of  the 
earth.  There  are  various  ways  of  getting  at  this  result,  but 
they  lie  rather  beyond  the  mathematical  scope  of  this  work. 

Its  density,  as  compared  with  that  of  the  earth,  is  found 
by  simply  dividing  its  mass  by  its  bulk  (both  as  compared 
with  the  earth) ;  i.e.,  the  sun's  density  equals  y/FoVA" 
=  0.255,  —  a  little  more  than  a  quarter  of  the  earth's  density. 

To  get  its  specific  gravity  (i.e.,  its  density  compared 
with  water),  we  must  multiply  this  by  the  earth's  mean 
specific  gravity,  5.53.  This  gives  1.41.  In  other  words, 
the  sun's  mean  density  is  only  about  1.4  times  that  of 
water,  —  a  very  significant  result  as  bearing  on  its  physical 
condition,  especially  when  we  know  that  a  considerable 
portion  of  its  mass  is  composed  of  metals. 

Of  course  this  low  density  depends  upon  the  fact  that  the  tem- 
perature is  enormously  high  and  the  materials  are  mainly  in  a  state 
of  cloud,  vapor,  or  gas. 


132 


LESSONS  IN  ASTRONOMY 


The  superficial  gravity  is  about  27.6  as  great  as  gravity 
on  the  earth ;  that  is  to  say,  a  body  which  weighs  one  pound 
on  the  surface  of  the  earth  would  there  weigh  27.6  pounds, 
and  a  person  who  weighs  150  pounds  here  would  there 
weigh  nearly  two  tons.  A  body  would  fall  444  feet  in  the 
first  second,  and  a  pendulum  which  vibrates  seconds  on  the 
earth  would  vibrate  in  less  than  a  fifth  of  a  second  there. 
162.  The  Sun's  Rotation.  —  Dark  spots  are  often  visible 
upon  the  sun's  surface,  passing  across  the  disk  from  east 

to  west  and  indicating  an 
axial  rotation.  The  aver- 
age time  occupied  by  a 
spot  in  passing  around 
the  sun  and  returning  to 
the  same  apparent  posi- 
tion, as  sejm__Jj-om  the 
earth,  is  about  27.25  days; 
different  observers,  how- 
ever, get  slightly  different 
results,  because,  as  we 
shall  see,  the  spots  are 
not  firmly  attached  to  the 
sun's  surface,  but  drift 
about  to  some  extent.  This  interval,-  however,  is  not 
the  true  time  of  the  sun's  rotation,  but  the  synodic,  as  is 
evident  from  Fig.  26.  Suppose  an  observer  on  the  earth 
at  E  sees  a  spot  on  the  center  of  the  sun's  disk  at  S ;  while 
the  sun  rotates  E  will  also  move  forward  in  its  orbit,  and 
the  observer,  the  next  time  he  sees  the  spot  on  the  center 
of  the  disk,  will  be  at  E',  the  spot  having  gone  around 
the  whole  circumference  plus  the  arc  SS1. 


FIG.  26.  —  Synodic  and  Sidereal  Revolu- 
tions of  the  Sun 


THE  SUN'S  ROTATION 


133 


The  equation  by  which  the  true,  or  sidereal,  period  is  deduced  from 
the  synodic  is  the  same  as  in  the  case  of  the  moon,  viz.  : 

1  =  1 -A, 

S~  T     E 

T  being  the  true  period  of  the  sun's  rotation,  E  the  length  of  the 
year,  and  S  the  observed  synodic  rotation.     This  gives'  T=  25.35. 

The  paths  of  the  spots  across  the  sun's  disk  are  usually 
more  or  less  oval,  showing  that  the  sun's  axis  is  inclined 
to  the  ecliptic,  and  so  inclined  that  the  north  pole  is  tipped 
about  7i°  towards  the  position  which  the  earth  occupies 


December  6 1*  March  6™  June  5*» 

FIG.  27.  —  Spot  Belts  and  Paths 


September  5th 


near  the  1st  of  September.  Twice  a  year  the  paths 
become  straight,  when  the  earth  is  in  the  plane  of  the 
sun's  equator,  June  3  and  December  5  (Fig.  27). 

163.    Peculiar   Law    of    the    Sun's    Rotation It   was 

noticed  quite  early  that  different  spots  give  different 
results  for  the  period  of  rotation,  but  the  researches  of 
Carrington,  half  a  century  ago,  first  brought  out  the 
fact  that  the  differences  are  largely  systematic,  so  that  at 
the  solar  equator  the  time  of  solar  rotation  is  less  than  on 
either  side  of  it.  For  spots  near  the  sun's  equator  it  is 
about  25  days;  for  solar  latitude  30°,  26.5  days  ;  and  in 
solar  latitude  40°,  27  days.  The  time  of  rotation  of  the  sun's 
surface  in  latitude  45°  is  fully  two  days  longer  than  at  the 


134  LESSONS  IN  ASTRONOMY 

equator;  but  we  are  unable  to  follow  the  law  further  towards 
the  poles  of  the  sun,  because  spots  are  almost  never  found 
beyond  the  parallel  of  45°,  though  faculse  which  have  been 
observed  in  higher  latitudes  give  substantially  the  same 
result,  as  do  certain  spectroscopic  observations. 

Possibly  this  equatorial  acceleration  may  be  due  in  some  way  to 
the  tremendous  outpour  of  heat  from  the  solar  surface,  as  Emdcn 
has  attempted  to  show  in  a  recent  paper.     The  more  general  impres- 
sion is,  however,  that  it  is  due  not 
to  any  causes  now  operating,  but  is  a 
lingering  survival  from  the  sun's  past 
history,    and    destined    ultimately  to 
disappear. 


164.  Study  of  the  Sun's  Suis 
face.  —  The  heat  and  light  of 
the  sun  are  so  intense  that  we 

FIG.  28.  —  Telescope  and  Screen  .  •  ,      ,      , .        J ,         J    . .        .  J , 

cannot  look  directly  at  it  with 

a  telescope,  as  we  do  at  the  moon,  and  it  is  necessary, 
therefore,  to  provide  either  a  special  eyepiece  with  suit 
able  shade-glass,  or  arrange  the  telescope,  as  in  Fig.  28, 
so  as  to  throw  an  image  of  the  sun  upon  a  screen. 

In  the  study  of  the  sun's  surface,  photography  is  for 
some  •  purposes  very  advantageous  and  much  used.  Tele- 
scopes are  often  made  with  lenses  specially  construct  rd 
for' photographic  operations,  since  an  object-glass  which 
would  give  admirable  results  for  visual  purposes  would 
be  worthless  photographically.  Visual  telescopes  may, 
however,  be  used  with  the  spectroheliograph  (see  Sec.  182*) 
for  photographing  the  sun  in  light  of  a  single  wave-length. 
The  exposure  required  for  a  photograph  is  practically 
instantaneous.  The  negatives  are  usually  from  two  inches 


STUDY  OF  THE   SUN'S  SURFACE:  135 

to  eight  or  ten  in  diameter,  and  some  of  the  best  of  them 
bear  enlarging  to  forty  inches. 

Photographs  have  the  great  advantage  of  freedom  from  prepos- 
session on  the  part  of  the  observer,  and  in  an  instant  of  time  they 
secure  a  picture  of  the  whole  surface  of  the  sun  such  as  would  require 


FIG.  29.  —  Greenwich  Photograph  of  Sun,  Sept.  10,  1898 

a  skillful  draftsman  hours  to  copy.  But,  on  the  other  hand,  they 
take  no  advantage  of  the  instants'  of  fine  seeing,  but  represent  the 
solar  surface  as  it  happened  to  appear  at  the  moment  when  the 
plate  was  uncovered,  aifected  by  all  the  momentary  distortions  due 
to  atmospheric  disturbances. 


136 


LESSONS  IN  ASTRONOMY 


165.  The  Photosphere.  —  The  sun's  surface  seen  with  a 
telescope,  under  a  medium  magnifying  power,  appears  to  be 
of  nearly  uniform  texture,  though  distinctly  darker  at  the 
edges,  and  usually  marked  here  and  there  with  certain  dark 


FIG.  30.  —  Nodules  and  Granules  on  the  Sun's  Surface 
After  Langley 

spots.  With  a  higher  power  it  is  evident  that  the  visible 
surface  (called  the  photosphere)  is  by  no  means  uniform, 
but  is  made  up,  as  shown  in  Fig.  30,  of  a  comparatively 
darkish  background  sprinkled  over  with  grains,  or  "nod- 
ules," as  Herschel  calls  them,  of  something  more  brilliant, — 


THE  PHOTOSPHERE  AND 


137 


"like  snowflakes  on  a  gray  cloth,"  according  to  Langley. 
These  nodules,  or  "  rice  grains,"  are  from  400  to  600  miles 
across,  and,  when  the  seeing  is  best,  themselves  break  up 
into  more  minute  "granules."  For  the  most  part,  the 
nodules  are  about  as  broad  as  they  are  long,  though  of 
irregular  form;  but  here  and  there,  especially  in  the 
neighborhood  of  the  spots,  they  are  drawn  out  into  long 
streaks,  known  as  "  filaments,"  "  willow  leaves,"  or  "  thatch 
straws." 

Certain  bright  streaks  called  "  faculse  "  are  also  usually 
visible  here  and  there  upon  the  sun's  surface,  and  though 
not  very  obvious 
near  the  center 
of  the  disk,  they 
become  con- 
spicuous near 
the  "  limb,"  or 
edge,  of  the  disk, 
especially  in  the 
neighborhood 
of  the  spots, 
as  shown  in 
Fig.  31.  These 
faculse  are  masses  of  the  same  material  as  the  rest  of 
the  photosphere,  but  elevated  above  the  general  level 
and  intensified  in  brightness.  When  one  of  them  passes 
off  the  edge  of  the  disk,  it  is  sometimes  seen  as  a  little 
projection.  The  fact,  however,  that  their  spectrum  shows 
bright  lines  of  calcium  vapor  makes  it  uncertain  whether 
they  may  not  be  clouds  of  that  substance  floating  high 
above  the  photosphere. 


FIG.  31.  — Spots  and  Faculae 
After  De  la  Rue 


138 


LESSONS  IN  ASTRONOMY 


sV*V 


In  their  nature,  the  photospheric  nodules  and  faculse 
are  generally  believed  to  be  luminous  clouds,  floating  in  a 
less  luminous  atmosphere,  just  as  a  snow  or  rain  cloud, 
which  has  been  formed  by  the  condensation  of  water- 
vapor,  floats  in  the  earth's  atmosphere.  Such  a  cloud, 
while  at  a  temperature  even  lower  than  that  of  the  sur- 
rounding gases,  has  a  vastly  greater  power  of  emitting 

light,  and  therefore, 
like  the  "  mantle  " 
of  a  Welsbach  gas- 
burner,  appears  very 
brilliant  in  compari- 
son with  the  gas  in 
which  it  floats. 
There  is  consider- 
able probability  that 
the  principal  ele- 
ment in  the  photo- 
sphere is  carbon. 
There  are,  however, 
some  serious  diffi- 
culties with  this 
cloud  theory, 
which  may  or  may 
not  be  removed  by  further  investigation. 

166.  Sun-Spots,  — —  Sun-spots,  whenever  visible,  are  the 
most  interesting  and  conspicuous  objects  upon  the  solar 
surface.  The  appearance  of  a  normal  sun-spot  (Fig.  32), 
fully  formed  and  not  yet  beginning  to  break  up,  is  that 
of  a  dark  central  "  umbra,"  more  or  less  circular,  with  a 
fringing  "penumbra"  composed  of  converging  filaments. 


FIG.  32.  —  Normal  Sun-Spot 
After  Secchi 


SUN-SPOTS  139 

The  umbra  itself  is  not  uniformly  dark  throughout,  but  is 
overlaid  with  filmy  clouds,  which  usually  are  rather  hard 
to  see,  but  sometimes  are  conspicuous,  as  in  the  figure. 
Usually,  also,  within  the  umbra  there  are  a  number  of 
round  and  very  black  spots,  sometimes  called  "  vortices," 
but  often  referred  to  as  "Dawes's  holes,"  after  the  name 
of  their  first  discoverer. 

Even  the  darkest  portions  of  the  umbra,  however,  are 
dark    only    by   contrast.     Photometric    observations    show 


FIG.  33.  — Group  of  Spots  from  a  Greenwich  Photograph,  Sept.  11,  1898 

(hat  the  nucleus  of  a  spot  gives  about  one  per  cent  as 
much  light  as  a  corresponding  area  of  the  photosphere ; 
the  blackest  portion  of  a  sun-spot  is  really  more  brilliant 
than  a  calcium  light. 

Very  few  spots    are    strictly  normal.     Frequently  the 
umbra  is  out  of   the  center  of   the  penumbra,  or  has  a 


140  LESSONS  IN  ASTRONOMY 

penumbra  on  one  side  only,  and  the  penumbral  filaments, 
instead  of  converging  regularly  towards  the  nucleus,  are 
often  distorted  in  every  conceivable  way.  Spots  are  often 
gathered  in  groups  within  a  common  penumbra,  separated 
from  each  other  by  brilliant  "  bridges,"  which  extend  across 
from  the  outside  photosphere.  Occasionally  a  spot  has  no 
penumbra  at  all,  and  sometimes  we  have  what  are  called 
"  veiled  "  spots,  in  which  there  seems  to  be  a  penumbra 
without  any  central  nucleus. 

167.  Nature  of  Sun-Spots.  —  Until  very  recently  sun- 
spots  have  been  believed  to  be  cavities  in  the  photosphere 
filled  with  gases  and  vapors,  cooler,  and  therefore  darker, 
than  the  surrounding  region.  This  theory  is  founded  on 
the  fact  that  many  spots  as  they  cross  the  sun's  disk 
behave  as  if  they  were  saucer-shaped  hollows,  with  sloping 
sides  colored  gray  and  the  bottom  black. 

This  theory  has,  however,  of  late  been  seriously  called 
in  question ;  many  spots,  possibly  a  majority,  as  shown  by 
photographs  and  drawings,  fail  to  present  the  appearances 
described.  Spectroheliograph  pictures  (Sec.  182*).  show 
that  there  is  a  whirling  motion  of  the  hydrogen  and  calcium 
vapors  that  lie  above  and  around  the  spots,  and  it  has 
been  suggested  that  sun-spots  are  really  something  like 
water-spouts  at  sea,  the  penumbra  of  the  spot  correspond- 
ing to  the  spreading  top,  the  darker  umbra  to  the  stem. 

Fig.  34,  copied  from  such  a  photograph  made  at  the 
Mt.  Wilson  Solar  Observatory,  January  5,  1917,  shows 
the  curvature  of  the  hydrogen  filaments  in  the  region 
surrounding  a  group  of  spots. 

In  the  neighborhood  of  the  spot  the  surrounding  photo- 
sphere is  usually  much  disturbed  and  elevated  into  faculse, 


NATURE  AND  DIMENSIONS  OF  SUN-SPOTS      141 

which  ordinarily  appear   before  the  spot  is  formed  and 
continue  after  it  disappears. 

168.  Dimensions  of  Sun-Spots,  etc.  —  The  diameter  of 
the  umbra  of  a  sun-spot  varies  all  the  way  from  500  miles, 
in  the  case  of  a  very  small  one,  to  50,000  miles,  in  the  case 
of  a  very  large  one.  The  penumbra  surrounding  a  group 


FIG.  34.  —Hydrogen  Flocculi  around  a  Sun-Spot 

of  spots  is  sometimes  150,000  miles  across,  though  that  is 
an  exceptional  size.  Quite  frequently  sun-spots  are  large 
enough  to  be  visible  with  the  naked  eye,  and  can  actually 
be  thus  seen  at  sunset  or  through  a  fog,  or  by  the  help 
of  a  colored  shade-glass. 

The  Chinese  have  many  records  of  such  objects,  but 
their  real  discovery  dates  from  1610,  as  an  immediate 
consequence  of  the  invention  of  the  telescope. 


142  LESSONS  IK  ASTRONOMY 

The  duration  of  sun-spots  varies  greatly,  but  they  are 
always  short-lived  phenomena,  from  the  astronomical  point 
of  view,  sometimes  lasting  only  for  a  few  days,  though 
more  frequently  for  a  month  or  two.  In  one  instance  a 
spot  group  attained  the  age  of  eighteen  months. 

As  to  their  cause,  positive  knowledge  is  still  wanting. 
Numerous  theories,  more  or  less  satisfactory,  have  been 
proposed.  Professor  Young,  the  author  of  our  text,  be- 
lieved them  to  be  the  effect  of  eruptions  breaking  through 
the  photosphere.  He  did  not,  however,  consider  them  to  be 
the  holes,  or  craters,  through  which  the  eruptions  break 
out,  as  Secchi  at  one  time  thought,  and  as  Mr.  Proctor 
maintained  to  the  very  last,  but  rather  thought,  in  accord- 
ance with  Secchi's  later  views,  that  when  an  eruption 
takes  place,  a  hollow,  or  sink,  results  in  the  neighboring 
cloud-surface,  and  in  this  hollow  the  cooler  gases  and 
vapors  collect.  It  has  been  generally  supposed  that  in 
some  way  they  are  due  to  matter  descending  from  above 
upon  the  photosphere,  although  recent  investigations  make 
it  seem  possible  that  they  are  due  to  ascending  currents  — 
material  flowing  outward  from  the  sun's  interior,  becom- 
ing cooler  at  the  higher  level,  and  therefore  appearing  dark 
against  the  brighter  photosphere. 

169.  Distribution  of  Spots,  and  their  Periodicity.  —  It  is 
a  significant  fact  that  the  spots  are  confined  mostly  to  two 
zones  of  the  sun's  surface  between  5°  and  40°  of  north 
and  south  solar  latitude.  Practically  none  are  ever  found 
beyond  the  latitude  of  45°,  but  at  the  time  when  spots  are 
most  numerous  a  few  appear  near  the  equator. 

In  1843  Schwabe  of  Dessau,  by  the  comparison  of  an 
extensive  series  of  observations  covering  nearly  twenty 


PERIODICITY  OF  SUN-SPOTS  143 

years,  showed  that  the  sun-spots  are  probably  periodic, 
being  at  some  times  much  more  numerous  than  at  others, 
with  a  roughly  regular  recurrence  every  ten  or  eleven 
years.  A  few  years  later  he  fully  established  this  remark- 
able result.  Wolf  of  Zurich  has  collected  all  the  observa- 
tions discoverable,  and  has  obtained  a  pretty  complete 
record  back  to  1610,  when  Galileo  first  discovered  these 
objects.  The  average  period  is  11.1  years,  but  the  maxima 
are  somewhat  irregular,  both  in  time  and  as  to  the  extent 
of  the  surface  covered  by  spots.  The  last  maximum 
occurred  in  1917. 

During  the  maximum  the  sun  is  never  without  spots, 
from  twenty-five  to  fifty  being  visible  at  once.  During 
the  minimum,  on  the  contrary,  weeks  and  even  months 
pass  without  the  appearance  of  a  single  one.  The  cause 
of  this  periodicity  is  not  yet  known. 

Another  curious  and  important  fact  has  recently  been  brought 
out  by  Spoerer,  though  not  yet  explained.  Speaking  broadly,  the 
disturbance  which  produces  the  spots  of  a  given  period  first  mani- 
fests itself  in  two  belts,  about  30°  north  and  south  of  the  sun's 
equator.  These  belts  then  draw  in  towards  the  equator,  and  the 
spot-maximum  occurs  when  their  latitude  is  about  16°;  while  the 
disturbance  finally  dies  out  at  a  latitude  of  from  5°  to  10°,  about 
twelve  or  fourteen  years  after  its  first  outbreak.  Two  or  three  years 
before  this  disappearance,  however,  two  new  zones  of  disturbance 
show  themselves.  Thus,  at  the  spot-minimum  there  are  usually  four 
well-marked  spot-belts :  two  near  the  sun's  equator,  due  to  the  expir- 
ing disturbance,  and  two  in  high  latitudes,  due  to  the  newly  begin- 
ning outbreak. 

170.    Terrestrial  Influence  of  Sun-Spots One  influence 

of  sun-spots  on  the  earth  is  perfectly  demonstrated. 
When  the  spots  are  numerous,  magnetic  disturbances 


144  LESSONS  IX  ASTRONOMY 

(magnetic  storms)  are  most  numerous  and  most  violent  upon 
the  earth,  —  a  fact  not  to  be  wondered  at,  since  notable 
disturbances  upon  the  sun's  surface  have  been  immediately 
followed  by  magnetic  storms  with  brilliant  exhibitions  of 
the  Aurora  Borealis,  as  in  1859  and  1883.  It  seems 
now  that  magnetic  disturbances  originate  in  the  sun  and 
travel  outward  in  certain  definite  directions.  When  such 
a  stream  strikes  the  earth,  we  have  a  magnetic  storm. 
But  it  may  pass  above  or  below,  and  this  explains  why 
a  spot  is  not  always  accompanied  by  a  disturbance  on 
the  earth. 

It  has  been  attempted,  also,  to  show  that  the  periodical  disturbance 
of  the  sun's  surface  is  accompanied  by  effects  upon  the  earth's  mete- 
orology,—  upon  its  temperature,  barometric  pressure,  storminess, 
and  the  amount  of  rainfall.  On  the  whole,  it  can  only  be  said  that 
while  it  is  possible  and  even  probable  that  real  effects  are  produced, 
they  must  be  very  slight,  and  are  almost  entirely  covered  up  by  the 
eif ect  of  purely  terrestrial  causes.  The  results  obtained  thus  far 
in  attempting  to  coordinate  sun-spot  phenomena  with  meteorological 
phenomena  are  unsatisfactory  and  often  contradictory.  We  may  add 
that  the  spots  cannot  produce  any  sensible  effect  by  their  direct  action 
in  diminishing  the  light  and  heat  of  the  sun.  They  do  not  directly 
alter  the  amount  of  solar  radiation  at  any  time  by  so  much  as  one 
part  in  a  thousand. 

THE   SOLAR   SPECTRUM   AND   ITS    REVELATIONS 

About  1860  the  spectroscope  appeared  in  the  field  as  a 
new  and  powerful  instrument  for  astronomical  research, 
resolving  at  a  glance  many  problems  which  before  did  not 
seem  even  open  to  investigation.  It  is  not  extravagant 
to  say  that  its  invention  has  done  almost  as  much  for 
astronomy  as  that  of  the  telescope  itself. 


PRINCIPLE  OF  THE   SPECTROSCOPE  145 

It  enables  us  to  study  the  light  of  distant  objects  and 
read  therein  a  record  more  or  less  complete  of  their 
chemical  composition  and  physical  conditions;  also  to 
measure  the  speed  with  which  they  are  approaching  or 
receding,  and  sometimes,  as  in  the  case  of  the  solar  promi- 
nences, to  observe  at  any  time  objects  otherwise  visible 
only  on  rare  occasions.  The  spectroscope  and  its  close 
ally,  the  photographic  plate,  have  together  given  us  "  the 
New  Astronomy." 

171.  Principle  of  the  Spectroscope.  —  The  essential  part 
of  the  apparatus  is  either  a  prism  or  a  train  of  prisms,  or 
else  a  diffraction  "  grating,"  *  which  is  capable  of  perform- 
ing the  same  office  of  "  dispersing  "  (i.e.,  of  spreading  and 
sending  in  different  directions)  the  rays  of  different  colors 
and  wave-lengths. 

If  with  such  a  "dispersion  piece,"  as  we  may  call  it 
(either  prism  or  grating),  one  looks  at  a  distant  point  of 
light,  he  will  see  instead  of  a  point  a  long,  bright  streak, 
red  at  one  end  and  violet  at  the  other.  If  the  object 
looked  at  is  a  line  of  light,  parallel  to  the  edge  of  the 
prism  or  to  the  lines  of  the  grating,  then  instead  of  a 
colored  streak  without  width,  he  gets  a  colored  band  or 
ribbon  of  light,  the  spectrum,  which  may  show  markings 
that  will  give  him  much  valuable  informaticn.  It  is 
usual  to  form  this  line  of  light  by  admitting  the  rays 
through  a  narrow  "slit"  placed  at  one  end  of  a  tube, 
which  carries  at  the  other  end  an  achromatic  object-glass 
having  the  slit  in  the  principal  focus.  This  tube,  with 

!The  "grating"  is  merely  a  piece  of  glass  or  speculum  metal,  ruled 
with  many  thousand  straight,  equidistant  lines,  from  5000  to  20,000  in 
the  inch. 


146 


LESSONS  IN   ASTRONOMY 


slit  and  lens,  constitutes  the  "  collimator."  Instead  of 
looking  at  the  spectrum  with  the  naked  eye,  it  is  better 
also  in  most  cases  to  use  a  small  "  view  telescope,"  so 
called  to  distinguish  it  from  the  large  telescope  to  which 
the  spectroscope  is  often  attached. 

172.    Construction  of  the  Spectroscope.  —  The  instrument, 
therefore,  as  usually  constructed,  and  shown  in  Fig.  35, 


Prism  Spectroscope 


Direct-Vision  Spectroscope 
FIG.  35.  —  Different  Forms  of  Spectroscope 

consists  of  three  parts,  —  collimator,  dispersion  piece,  and 
view  telescope,  —  although  in  the  "  direct-vision  "  spectro- 
scope, shown  in  the  figure,  the  view  telescope  is  omitted. 
If  the  slit  S  be  illuminated  by  strictly  homogeneous  light 
(i.e.,  light  all  of  one  color),  say  yellow,  the  "real  image" 
of  the  slit  will  be  found  at  Y.  If,  at  the  same  time,  light 
of  a  different  color  —  red,  for  instance  —  be  also  admitted, 


THE   SOLAR  SPECTRUM 


147 


i  second  image  will  be  formed  at  7£,  and  the  observer  will 
then  see  a  spectrum  consisting  of  two  bright  lines,  one 
yellow,  the  other  red,  which  are  really  nothing  more  than 
images  of  the  slit. 

If  violet  light  be  admitted,  a. third  image  will  be  formed 
at  F,  and  there  will  be  three  bright  lines.  If  light  from 
a  candle  be  admitted,  there  will  be  an  infinite  number  of 
these  slit-images  close  together,  like  the  pickets  in  a  fence, 
without  interval  or  break,  and  we  then  get  what  is  called 
a  "  continuous  "  spectrum. 

If,  however,  we  look  at  sunlight  or  moonlight  or  the  light 
of  a  star,  we  shall  find  a  spectrum  continuous  in  the  main, 


FIG.  36.  —  Small  Portion  of  Solar  Spectrum  (green) 
Photographed  by  Higgs 

but  crossed  by  thousands  of  dark  lines,  or  missing  slit-images 
(as  if  some  of  the  fence  pickets  had  been  destroyed,  leav- 
ing gaps  in  the  series).  The  cause  of  these  dark  lines, 
first  noticed  by  Wollaston  in  1800,  but  later  and  inde- 
pendently discovered  and  carefully  observed  by  Fraunhofer 
in  1814,  was  a  mystery  for  nearly  fifty  years,  until  the 
epoch-making  work  of  Kirchhoff. 

173.  Principles  upon  which  Spectrum  Analysis  depends.  — 
These,  substantially,  as  announced  by  Kirchhoff  in  1858, 
are  the  three  following: 

1 .    A  continuous  spectrum  is  given  by  bodies  which  are  so 
dense  that  the  molecules  interfere  with  each  other  in  such  a 


148  LESSONS  IN   ASTRONOMY 

way  as  to  prevent  their  free  vibration  ;  i.e.,  by  bodies  which 
are  either  solid  or  liquid,  or,  if  gaseous,  are  under  pressure. 

2.  The  spectrum  of  a  luminous  gas  under  low  pressure 
is  discontinuous,  that  is,  it  is  made  up  of  bright  lines  or 
bands,  and  these  lines  are -characteristic.  The  same  sub- 
stance under  similar  conditions  always  gives  the  same  set 
of  lines,  and  usually  it  does  so  even  under  conditions  which 
differ  rather  widely;  but  when  the  circumstances  differ 
too  much,  it  may  give  two  or  more  different  spectra. 

3  (and  most  important  for  our  purpose  just  now).  A 
gas  or  vapor  absorbs  from  a  beam  of  white  light  passing 
through  it  precisely  those  rays  of  which  its  own  spectrum  con- 
sists ;  so  that  the  spectrum  of  white  light  which  has  been 
transmitted  through  such  a  vapor,  if  the  vapor  is  cooler 
than  the  original  source  of  light,  exhibits  a  "reversed" 
spectrum  of  the  gas ;  i.e.,  we  get  a  spectrum  which  shows 
dark  lines  in  place  of  the  characteristic  bright  lines,  as  in 
the  spectrum  of  sunlight. 

We  therefore  infer  that  the  sun  is  covered  by  an 
envelope  of  gases,  not  so  hot  as  the  luminous  clouds 
which  form  the  photosphere,  and  that  these  gases  by  their 
absorption  produce  the  dark  lines  in  its  spectrum. 

174.  Experiment  illustrating  Reversal  of  Spectrum.  — 
The  principle  of  reversal  is  illustrated  by  Fig.  37.  Sup- 
pose that  in  front  of  the  spectroscope  we  place  a  spirit  lamp 
with  a  little  carbonate  of  soda  and  some  salt  of  thallium 
upon  the  wick.  We  shall  then  get  a  spectrum  showing  the 
two  yellow  lines  of  sodium  and  the  green  line  of  thallium,  all 
bright,  as  in  the  upper  of  the  two  spectra.  If  now  the  lime- 
light be  started  behind  the  flame,  we  shall  at  once  get  the 
effect  shown  in  the  lower  figure,  —  a  continuous  spectrum 


REVERSAL  OF  SPECTRUM  LINES 


149 


Screen 


crossed  by  three  black  lines  which  exactly  replace  the 
brighter  ones.  Thrust  a  screen  between  the  lamp  flame  and 
the  lime,  and  the  dark  lines  instantly  turn  bright  again. 

The  dark  lines  which  appear  when  the  screen  is  removed  are  dark 
only  relatively  to  the  background:  when  the  screen  is  taken  away  they 
really  brighten  a 
little  (say  two  or 
three  per  cent); 
but  the  brightness 
of  the  background 
increases  hundreds 
of  times,  and  so  far 
exceeds  that  of  the 
lines  themselves 
that  they  look 
black.  The  dark 
lines  of  the  solar 
spectrum  are  really 
bright,  and  can  be 
photographed  as 
such  by  arranging 
matters  so  that 
one  of  them  shall 
fall  upon  a  nar- 


FIG.  37.  —  Reversal  of  the  Spectrum 


row  slit  in  a  diaphragm  which  excludes  all  the  brighter  background. 

175.    Chemical  Constituents  of  the  Solar  Atmosphere.  - 
By  taking  advantage  of  these  principles  we  can  detect 
a   large    number   of    well-known    terrestrial   elements   in 
the    sun   by   means  of   the  dark  lines1  in  its  spectrum, 

1  They  are  generally  referred  to  as  Fraunhofer's  lines,  because  Fraun- 
hofer  was  the  first  to  map  them.  To  some  of  the  principal  ones  he 
assigned  letters  of  the  alphabet,  which  are  still  retained ;  thus,  A  is  a 
strong  red  line  at  the  extreme  end  of  the  spectrum ;  (7,  one  in  the  scarlet ; 
D,  one  in  the  yellow ;  and  H,  one  in  the  violet. 


150 


LESSONS  IN  ASTRONOMY 


which,  in  an  instrument  of  high  power,  number  several 
thousand. 

By  proper  arrangements  it  is  possible  to  identify  among 
these  lines  many  which  are  due  to  the  presence  in  the  sun's 
atmosphere  of  known  terrestrial  elements  in  the  state  of 
vapor.  To  effect  the  comparison  necessary  for  this  purpose, 
the  spectroscope  must  be  so  arranged  that  the  observer  can 
confront  the  spectrum  of  sunlight  with  that  of  the  sub- 
stance to  be  tested.  In  order  to  do  this,  half  of  the  slit  is 
covered  by  a  little  reflector,  or  "  comparison  prism,"  which 
reflects  into  the  tube  the  light  of  the  sun,  while  the  other 


FIG.  38.  — Photographic  Comparison  of  the  Solar  Spectrum  with  that  of  Iron 

Trowbridge 

half  of  the  slit  receives  directly  the  light  of  some  flame 
or  electric  spark.  On  looking  into  the  spectroscope  the 
observer  will  then  see  a  spectrum,  the  lower  half  of  which, 
for  instance,  is  made  by  sunlight,  while  the  upper  half  is 
made  by  light  coming  from  an  electric  spark  between  two 
metal  points,  say  of  iron.  This  latter  spectrum  will  show 
the  bright  lines  of  iron  vapor,  and  the  observer  can  then 
easily  see  whether  they  do  or  do  not  correspond  exactly 
with  the  dark  lines  of  the  solar  spectrum. 

In  such  comparisons  photography  may  be  most  effectively  used 
instead  of  the  eye.  Fig.  38  is  an  excellent  reproduction,  on  a  reduced 
scale,  of  a  negative  made  by  Professor  Trowbridge  of  Cambridge. 


ELEMENTS  DISCOVERED  IN  THE  SUN  151 

The  lower  half  is  the  violet  portion  of  the  sun's  spectrum,  and  the 
upper  half  the  corresponding  portion  of  that  of  an  electric  arc  charged 
with  the  vapor  of  iron.  (In  the  negative  the  dark  lines,  of  course,  are 
bright,  and  vice  versa.}  The  reader  can  see  for  himself  with  what 
absolute  certainty  such  a  photograph  indicates  the  presence  of  iron 
in  the  solar  atmosphere.  A  few  of  the  lines  in  the  photograph  which 
do  not  show  corresponding  lines  in  the  solar  spectrum  are  due  to 
other  substances  than  iron. 

176.  Elements  known  to  exist  in  the  Sun. — As  the  result 
of  such  comparisons  we  have  the  following  list  of  thirty- 
six  elements  which  are  now  known  to  exist  in  the  sun. 

*  Calcium,  11.  *  Strontium,  23.  Copper,  30. 

*  Iron.  1.  Vanadium,  8.  Zinc,  29. 

*  Hydrogen,  22.  *  Barium,  24.  Cadmium,  26. 

*  Sodium,  20.  ,         Carbon,  7.  *  Cerium,  10. 

*  Nickel,  2.  Scandium,  12.  Glucinum,  33. 

*  Magnesium,  19.  Yttrium,  15.  Germanium,  32. 

*  Cobalt,  6.                          Zirconium,  9.  Rhodium,  27. 
Silicon,  21.                       Molybdenum,  17.  Silver,  31. 
Aluminium,  25.               Lanthanum,  14.  Tin,  34. 

*  Titanium,  3.  Niobium,  16.  Lead,  35. 

*  Chromium,  5.  Palladium,  18.  Erbium,  28. 

*  Manganese,  4.  Neodymium,  13.  Potassium,  36. 

The  substances  are  arranged  according  to  the  intensity  of  the  dark 
lines  by  which  they  are  represented  in  the  solar  spectrum,  while  the 
numbers  appended  indicate  the  rank  which  each  would  hold  if  the 
arrangement  had  been  based  upon  the  number  of  lines.  An  asterisk 
denotes  that  the  lines  of  the  element  often  or  always  appear  as  bright 
lines  in  the  spectrum  of  the  chromosphere  (Sec.  180).  To  these 
elements  must  be  added  Helium  (Sec.  181),  which  gives  no  dark 
lines  in  the  spectrum  of  the  photosphere,  but  does  give  several 
conspicuous  bright  lines  in  that  of  the  chromosphere. 

In  the  atmosphere  of  the  sun  these  bodies  must  be,  of 
course,  in  the  condition  of  vapor,  which  is  somewhat  cooler 


152  LESSONS  IN  ASTRONOMY 

than  the  clouds  which  form  the  photosphere.  It  will  be 
noticed  that  all  of  them,  carbon  and  hydrogen  alone 
excepted,  are  metals,  and  that  a  number  of  the  elements 
which  are  among  the  most  important  in  the  constitution 
of  the  earth  fail  to  present  themselves.  Thus  far  chlorine, 
bromine,  iodine,  sulphur,  and  phosphorus  all  appear  to  be 
missing,  and  the  indications  of  oxygen  (which  forms  fully 
half  the  mass  of  the  earth's  crust)  are  very  feeble.  Nitrogen 
probably  exists  in  combination  with  carbon. 

We  must  be  cautious,  however,  in  drawing  negative 
conclusions.  It  is  quite  possible  that  the  spectra  of  these 
bodies  under  solar  conditions  may  be  so  different  from  their 
spectra  as  presented  in  our  laboratories,  that  we  cannot 
easily  recognize  them:  many  substances,  under  different 
conditions,  give  two  or  more  widely  different  spectra. 

177.  The  Reversing  Layer.  —  According  to  Kirchhoff's 
theory,  the  dark  lines  are  most  of  them1  formed  by  the 
passing  of  light  emitted  by  the  minute  solid  or  liquid 
particles  of  the  photospheric  clouds  through  the  somewhat 
cooler  vapors  which  compose  the  substances  that  we  recog- 
nize by  the  dark  lines  in  the  spectrum.  If  this  is  so,  the 
spectrum  of  the  gaseous  envelope,  which  by  its  absorption 
forms  the  dark  lines,  ought  to  show  a  spectrum  of  corre- 
sponding bright  lines  when  seen  by  itself.  The  opportu- 
nities are  rare  when  it  is  possible  to  obtain  a  spectrum  of 

1  Among  the  thousands  of  lines  in  the  solar  spectrum  a  considerable 
number  originate  in  the  atmosphere  of  the  earth.  They  are  mostly  due 
to  oxygen  and  water-vapor,  and  are  especially  abundant  in  the  red  and 
yellow  portions  of  the  spectrum.  These  "  telluric  "  lines  are  easily  distin- 
guished by  the  fact  that  they  become  extremely  conspicuous  when  the 
sun  is  near  the  horizon,  but  are  feeble  when  he  is  near  the  zenith ;  and 
they  also  vary  with  the  dryness  of  the  air. 


THE  REVERSING  LAYER  153 

this  gaseous  envelope  separate  from  that  of  the  photo- 
sphere ;  but  at  the  time  of  a  total  eclipse,  at  the  moment 
when  the  sun's  disk  has  just  been  obscured  by  the  moon, 
and  the  sun's  atmosphere  is  still  visible  beyond  the  moon's 
limb,  the  observer  ought  to  see  this  bright-line  spectrum, 
if  the  slit  of  the  spectroscope  be  carefully  directed  to  the 
proper  point ;  and  the  observation  has  actually  been  made. 
The  lines  of  the  solar  spectrum,  which  up  to  the  time  of  the 
total  obscuration  of  the  sun  remain  dark  as  usual,  are 
suddenly  reversed,  and  the  whole  field  of  the  spectroscope 
is  filled  with  brilliant  colored  lines,  which  flash  out  quickly, 
and  then  gradually  fade  away,  disappearing  in  about  two 
seconds. 

The  natural  interpretation  of  this  phenomenon  is  that 
the  formation  of  the  dark  lines  in  the  solar  spectrum  is, 
mainly  at  least,  produced  by  a  very  thin  stratum  closely 
covering  the  photosphere,  since  the  moon's  motion  in 
two  seconds  would  correspond  to  a  thickness  of  only 
500  miles. 

This  observation,  first  made  by  the  author  in  1870,  remained 
long  uncorroborated,  but  received  a  beautiful  photographic  confirm- 
ation in  1896.  Mr.  Shackleton,  the  photographer  of  an  English 
party  which  observed  the  eclipse  of  that  year  in  Nova  Zembla, 
obtained  a  photograph  of  the  spectrum  at  the  critical  moment  with 
an  exposure  of  less  than  half  a  second,  and  found  it  just  as  described, 
showing  several  hundreds  of  bright  lines  which  correspond  to  the 
dark  Fraunhofer  lines.  A  second  photograph,  made  only  five  or 
six  seconds  later,  shows  only  some  twenty  lines,  well  known  as 
belonging  to  the  spectrum  of  the  chromosphere  and  prominences. 
Similar  results  for  the  "  flash  spectrum,"  as  it  is  called,  were  also 
obtained  by  various  observers  during  the  eclipses  of  January,  1898, 
May,  1900,  and  May,  1901,  with  instruments  of  still  higher  power 
than  that  of  Mr.  Shackleton. 


154 


LESSONS  IN  ASTRONOMY 


There  are  reasons,  however,  to  doubt  whether  the  lines  are  all 
produced  in  such  a  thin  layer.  According  to  Sir  Norman  Lockyer, 
the  solar  atmosphere  is  very  extensive,  and  certain  lines  of  the  spec- 
trum appear  to  be  formed  only  in  the  regions  of  lower  temperature 
high  above  the  surface  of  the  photosphere.  It  is  probable  also  that 
many  lines  originate  within  the  photosphere  and  not  above  it,  being 
caused  by  the  vapors  which  lie  between  the  cloud  masses  that  give 
the  brilliant  light. 

178.  Sun-Spot  Spectrum.  —  The  spectrum  of  a  sun-spot 
differs  from  the  general  solar  spectrum  not  only  in 
its  diminished  brilliancy,  but  in  the  great  widening  of 
certain  lines,  the  thinning  of  others,  and  the  change 
of  some  (especially  the  lines  of  hydrogen)  to  bright 

lines  on  some   occasions. 
i  The  majority  of  the  Fraun- 

hofer  lines,  however,  are 
not  much  affected  either 
way. 

In  the  green  and  blue 
portions  of  the  spectrum 
the  darkest  part  of  a  sun- 
spot  spectrum  is  found  to  be  composed  of  fine  dark 
lines  close  packed.  This  shows  that  the  darkening  is 
due  to  the-  absorption  of  light  by  gases  and  vapors,  not 
by  mist  or  smoke,  for  then  the  spectrum  would  be 
continuous. 

Sometimes,  in  connection  with  sun-spots,  certain  lines 
of  the  spectrum  are  bent  and  broken,  as  shown  in 
Fig.  39.  These  distortions  are  explained  by  the  swift 
motion  towards  or  from  the  observer  of  the  gaseous  mat- 
ter, which  by  its  absorption  produces  the  line  in  question. 
In  the  case  illustrated  in  the  figure  hydrogen  was  the 


FIG.  39.  —The  C  line  in  the  Spectrum 
of  a  Sun-Spot 


DOPPLER-FIZEAU  PBINCIPLE  155 

substance,  and  its  motion  was  from  the  observer,  —  nearly 
300  miles  a  second  at  one  point. 

179.    Doppler's   Principle The  principle  upon  which 

the  explanation  of  this  displacement  and  distortion  of 
lines  depends  was  first  enunciated  by  Doppler  in  1842. 
It  is  this  :  When  the  distance  between  us  and  a  body  which 
is  emitting  regular  vibrations,  either  of  sound  or  of  light,  is 
decreasing,  then  the  number  of  pulsations  received  by  us 
in  each  second  is  increased,  and  the  length  of  the  waves  is 
correspondingly  diminished.  Thus,  the  pitch  of  a  musical 
tone  rises  in  the  case 
supposed;  and  in  the 
same  way  the  refrangi- 
bility  of  a  light- wave, 
which  depends  upon 
its  wave-length,  is  in- 

FIG.  40.  —The  Doppler-Fizeau  Principle 

creased,  so  that  it  will 

fall  nearer  the  violet  end  of  the  spectrum.  This  principle 
finds  numerous  applications  in  modern  astronomical  spec- 
troscopy,  and  it  is  of  extreme  importance  that  the  student 
should  clearly  understand  it.  In  its  astronomical  applica- 
tions it  is  often  called  the  JDoppler-Fizeau  principle  because 
Fizeau  first  called  attention  to  the  shift  that  would  be 
produced  in  the  lines  of  a  spectrum. 

Fig.  40  illustrates  the  principle.  The  lower  strip  is  a  small  por- 
tion of  the  yellow  part  of  the  spectrum  of  an  imaginary  star,  and 
the  upper  the  corresponding  part  of  the  spectrum  of  sodium  with 
which  it  is  compared.  The  shift  of  the  lines  of  the  star  spectrum 
indicates  that  it  is  coming  nearer  at  the  rate  of  nearly  fifty  miles 
a  second  ;  some  stars  move  faster. 

It  was  discovered  in  1895,  by  Humphreys  and  Mohler  at  Baltimore, 
that  increase  of  pressure  causes  the  lines  in  the  spectrum  of  a  luminous 


156  LESSONS  IN  ASTRONOMY 

gas  to  shift  slightly  towards  the  red,  very  much  as  if  the  gas  were 
receding,  though  not  according  to  the  same  simple  law.  The  shift  is 
very  slight,  however,  for  pressures  not  exceeding  200  or  300  pounds  to 
the  inch ;  but  it  is  quite  possible  that  in  cases  of  explosion  the  pres- 
sures would  be  sufficient  to  cause  large  displacements.  (See  Sec.  355.) 

180.  The  Chromosphere.  —  Outside  the  photosphere,  or 
shining  surface  of  the  sun,  lies  the  so-called  chromosphere, 
of  which  the  stratum  of  gases  that  produce  the  dark  lines 
in  the  solar  spectrum  is  the  hottest  and  densest  portion. 
The  word  is  derived  from  the  Greek,  chroma  (color),  and 
means  "  color  sphere."     It  is  so  called  because  it  is  bril- 
liantly scarlet,  owing  this  color  to  the  hydrogen  gas  which 
is  its  most  conspicuous  component.     In  structure  it  is  like 
a  sea  of  flame  covering  the  photosphere  to  a  depth  of  from 
5000  to  10,000  miles,  and  seen  through  a  telescope  at  the 
time  of  a  total  eclipse  has  been  well  described  as  looking 
like    a    "prairie    on   fire."     There    is,    however,   no  real 
burning  in  the  case,  i.e.,  no  heat-producing  combination 
of  hydrogen  with  oxygen  or  with  any  other  element. 

Under  ordinary  circumstances  the  chromosphere  is  invisi- 
ble, drowned  in  the  light  of  the  photosphere.  It  can  be 
seen  with  the  telescope  for  only  a  few  seconds  at  a  time, 
during  the  fleeting  moments  of  a  total  eclipse ;  but  with 
the  spectroscope  it  can  be  studied  at  other  times,  as  we 
shall  see. 

181.  Prominences   and  their   Spectrum.  —  The    promi- 
nences, or  protuberances,  are  scarlet  clouds  which  are  seen 
during  a  total  eclipse,  projecting  from  behind  the  edge  of 
the  moon.     They  are  simply  extensions   of  the  chromo- 
sphere, or  isolated  clouds  of  the  same  gaseous  substances, 
chiefly  hydrogen,  their  true  nature  having  been  established 


T11E  PROMINENCES  157 

at  an  eclipse  in  1868,  when  their  spectrum  was  first  satis- 
factorily observed.  It  is  composed  of  numerous  bright 
lines,  conspicuous  among  which  are  the  lines  of  hydrogen, 
together  with  a  brilliant  yellow  line  (sometimes  called  D3 
because  near  the  two  so-called  D  lines)  and  the  so-called  H 
and  K  lines  of  calcium,  with  a  number  of  others  that  are 
always  present  though  more  difficult  to  observe.  At  times 
also  when  the  solar  forces  are  peculiarly  energetic  hundreds 
of  other  lines  appear,  especially  those  of  iron,  titanium, 
magnesium,  and  sodium. 

For  a  long  time  the  D3  line  remained  entirely  unidenti- 
fied, and  the  name  of  helium,  or  "  sun-metal,"  was  proposed 
and  accepted  for  the  hypothetical  element  to  which  it  was 
supposed  to  be  due.  In  1895,  however,  Dr.  Ramsay,  one 
of  the  discoverers  of  argon,  found  the  D3  line  in  the 
spectrum  of  a  gas  disengaged  by  heating  and  pumping 
from  a  rare  mineral  known  as  uraninite,  and  very  soon 
the  new  gas  was  found  by  him  and  other  observers  in 
various  other  minerals  and  in  meteoric  iron.  Along  with 
the  D3  line  were  also  found  in  the  spectrum  of  the  gas  a 
number  of  other  unidentified  lines  of  the  chromosphere 
spectrum,  and  these  also  appear  with  D3  and  the  hydrogen 
lines  in  the  spectra  of  certain  nebulse  and  stars. 

It  was  a  great  triumph  thus  to  "  run  helium  to  earth," 
though  as  yet  very  little  is  known  as  to  its  nature  and 
properties  except  that,  next  to  hydrogen,  it  is  the  lightest 
of  all  known  gases,  in  chemical  inertness  appears  to 
resemble  argon  itself,  and  thus  far  is  the  only  gas  which 
resists  liquefaction. 

182.  Spectroscopic  Observations  of  the  Prominences  and 
Chromosphere.  —  Since  the  spectrum  of  these  objects  is 


158 


LESSONS  IN   ASTRONOMY 


composed  of  a  small  number  of  brilliant  lines,  it  is  possible 
to  observe  them  with  a  spectroscope  in  full  daylight.  The 
explanation  of  the  way  in  which  the  spectroscope  effects 
this  lies  rather  beyond  our  limitations ;  but  it  is  sufficient 
for  our  purpose  to  say  that  by  attaching  a  spectroscope 


FIG.  41.  —  Prominences 

1.  Quiescent  Prominences  2.  Quiescent  Prominences 

3.  Eruptive  Prominences  — Flames 

4.  Eruptive  Prominences  —  Jets  and  Spikes  near  Sun's  Limb,  Oct.  5, 1871 

to  a  good  telescope  the  prominences  can  now  be  studied 
at  leisure  any  clear  day.  They  are  wonderfully  interest- 
ing and  beautiful  objects.  Some  of  them,  the  so-called 
"  quiescent "  prominences,  are  of  enormous  size,  50,000  or 
even  100,000  miles  in  height,  faint  and  diffuse,  remaining 


PHOTOGRAPHY  OF   PROMINENCES  159 

almost  unchanged  for  days.  Others  are  much  more 
brilliant  and  active,  especially  those  that  are  associated 
with  sun-spots,  as  many  of  them  are.  These  "  eruptive  " 
prominences  often  alter  their  appearance  very  rapidly,  — 
so  fast  that  one  can  sometimes  actually  see  the  motion  : 
velocities  from  50  to  200  miles  a  second  are  frequently 
met  with.  As  a  rule  the  eruptive  prominences  are  not  so 
large  as  the  quiescent  ones,  but  occasionally  they  surpass 


10.34  10.40  10.58 

FIG.  42.  —  Photographs  of  Prominences,  March  25,  1895 

After  Hale 

them,  and  a  few  have  been  observed  to  attain  elevations 
of  more  than  200,000  miles.  Fig.  41  gives  specimens  of 
both  kinds. 

182*.  Photography  of  Prominences.  —  Quite  recently  it 
has  become  possible  to  photograph  these  objects  at  any 
time  by  utilizing  the  H  and  K  lines  in  their  spectrum. 
An  explanation  of  the  method  lies  quite  beyond  our 
scope,  but  Professor  Hale,  the  director  of  the  new  Yerkes 
Observatory,  and  Deslandres  in  Paris,  have  been  spe- 
cially successful  in  this  line,  and  both  have  constructed 


160  LESSONS  IN  ASTRONOMY 

spectroscopic  apparatus  with  which,  at  a  single  operation, 
they  obtain  a  picture  of  the  entire  chromosphere  arid  its 
prominences  surrounding  an  image  of  the  sun  itself  with  its 
spots  and  faculous  regions.  The  solar  image  is  really  only 
a  picture  of  those  parts  of  the  disk  where  the  calcium  lines 
are  bright,  and  reveals  the  presence  of  clouds,  or  "  flocculi," 
of  glowing  calcium,  at  a  somewhat  higher  level  than  the 
photosphere.  Similar  photographs  are  obtained  in  "  hydro- 
gen light,"  so  that  we  may  now  learn  something  of  the 
distribution  of  these  elements  in  the  sun.  The  new  method 
is  a  great  step  in  the  study  of  solar  physics.  Fig.  42  is  from 
one  of  Hale's  photographs  and  illustrates  well  the  rapidity 
with  which  the  prominences  rise  and  change  their  forms. 

183.  The  Corona.  —  Probably  the  most  beautiful  and 
impressive  of  all  natural  phenomena  is  the  corona,  the 
"glory"  of  light  which  surrounds  the  sun  at  a  total 
eclipse.  The  portion  of  it  near  the  sun  is  dazzlingly  bright 
and  of  a  pearly  luster,  contrasting  beautifully  with  the 
scarlet  prominences,  which  stud  it  like  rubies.  It  seems 
to  be  mainly  composed  of  projecting  filaments  of  light, 
which  near  the  sun  are  pretty  well  defined,  but  at  a  little 
distance  fade  out  and  melt  into  the  general  radiance. 
Near  the  poles  of  the  sun  the  corona  does  not  usually 
extend  very  far  and  has  a  pretty  definite  outline,  but  in 
the  spot  regions  and  near  the  sun's  equator  faint  streams 
sometimes  extend  to  a  distance  of  several  degrees ;  and  at 
the  distance  of  the  sun  every  degree  means  more  than  a 
million  and  a  half  of  miles. 

A  very  striking  and  perplexing  feature  is  the  existence 
of  dark  rays  or  rifts,  which  reach  clear  down  to  the  very 
edge  of  the  sun. 


THE   CORONA  161 

The  corona  varies  greatly  in  brightness  at  different 
eclipses,  according  to  the  apparent  diameter  of  the  moon 
at  the  time.  The  portion  of  the  corona  nearest  the  sun 
is  so  much  brighter  than  the  outer  regions  that  a  little 
increase  of  the  moon's  diameter  cuts  off  a  very  large  pro- 
portion of  the  light.  The  total  light  of  the  corona  is 
usually  at  least  two  or  three  times  as  great  as  that  of  the 
full  moon.  Fig.  43  is  from  a  photograph  of  the  eclipse 


FIG.  43.  — Corona  of  Eclipse  of  1900,  Wadesboro,  N.C. 

of  May,  1900,  made  at  Wadesboro,  N.C.  At  that  time 
the  sun-spots  were  at  their  minimum,  and,  as  is  then 
usual,  the  equatorial  "wings"  were  very  long  and  the 
polar  streamers  especially  numerous  and  well  defined. 

184.  Spectrum  of  the  Corona.  —  A  characteristic  feature 
of  its  spectrum  is  a  bright  green  line.  This  line  was  at 
first,  and  for  a  long  time,  supposed  to  coincide  with  the 
"  1474  "  line  of  Kirchhoff's  map  of  the  spectrum  —  a  very 
puzzling  circumstance,  as  that  line  is  due  to  iron,  and  iron 


162  LESSONS  IN  ASTRONOMY 

vapor  seemed  to  be  a  veiy  improbable  substance  to  be 
found  at  such  an  elevation  above  the  hydrogen  of  the 
chromosphere.  Photographs  of  the  corona  spectrum  made 
in  1896  and  at  the  later  eclipses  have,  however,  shown 
that  the  supposed  coincidence  with  1474  was  a  mistake, 
the  corona  line  being  slightly  more  refrangible  and  nearer 
the  blue  end  of  the  spectrum.  The  photographs  have 
also  detected  several  other  lines  in  the  violet  and  ultra- 
violet, and  it  is  now  clear  that  the  green  line  and  the 
others  are  due  to  some  still  unknown  gaseous  element 
(probably  lighter  than  hydrogen),  which  has  been  provi- 
sionally called  coronium,  after  the  analogy  of  helium.  It  is 
to  be  hoped  that  before  very  long  this  substance  also  may 
be  "  run  to  earth  "  as  helium  has  been. 

185,  The  corona  is  proved  to  be  a  true  appendage  of 
the  sun,  and  not,  as  has  been  at  times  supposed,  a  mere 
optical  phenomenon,  nor  one  due  to  the  atmosphere  of  the 
earth  or  moon,  by  two  established  facts : 

1st.  That  its  spectrum  is  not  that  of  reflected  sunlight, 
but  of  a  self-luminous  gas ;  and 

2d.  Because  photographs  of  the  corona,  made  at  widely 
different  stations  along  the  track  of  an  eclipse,  agree  closely 
in  details. 

Its  real  nature  and  relation  to  the  sun  are  very  difficult 
to  explain.  It  is  a  gaseous  envelope,  at  least  largely  gas- 
eous, for  it  may,  and  probably  does,  contain  much  "  dust " 
and  "  fog."  It  does  not,  however,  stand  in  any  such  rela- 
tio'n  to  the  globe  below  as  does  our  atmosphere,  since  its 
streamers  strongly  indicate  that  it  is  not  in  equilibrium 
under  the  sun's  attraction,  but  is  largely  maintained  and 
shaped  by  powerful  repulsive  forces. 


THE  SUN'S  LIGHT  163 

Its  phenomena  are  not  yet  satisfactorily  explained,  and 
remind  us  far  more  of  auroral  streamers  and  of  comets' 
tails  than  of  anything  that  occurs  in  the  lower  regions  of 
the  earth's  atmosphere.  (See,  however,  Sec.  306.) 

Its  material  is  of  excessive  rarity,  as  is  shown  by  the 
fact  that  in  a  number  of  cases  comets  have  passed  directly 
through  it  (as,  for  instance,  in  1882)  without  the  slightest 
perceptible  disturbance.  Its  density,  therefore,  must  be 
almost  inconceivably  less  than  that  of  the  best  air-pump 
vacuum  which  we  are  able  to  produce. 

THE  SUN'S  LIGHT  AND  HEAT 

186.  The  Sun's  Light.  —  By  photometric  measures,  which 
we  cannot  explain  here,  it  is  found  that  the  sun  gives  us 
about  1575  billions  of  billions  (1575  followed  by  24  ciphers) 
times  as  much  light  as  a  standard  candle1  would  do  at 
that  distance. 

The  amount  of  light  received  from  the  sun  is  about 
600,000  times  that  given  by  the  full  moon,  about 
7000,000000  times  that  of  Sirius,  the  brightest  of  the 
fixed  stars,  and  fully  200000,000000  times  that  of  the 
Pole-star. 

As  to  the  intensity  of  sunlight,  or  the  intrinsic  brightness 
of  the  sun's  surface,  we  find  that  it  is  about  190,000 
times  as  bright  as  that  of  the  candle  flame,  and  fully 
150  times  as  bright  as  the  lime  of  a  calcium  light;  so 
that  even  the  darkest  part  of  a  sun-spot  outshines  the 

1  The  standard  candle  is  a  sperm  candle  weighing  one-sixth  of  a  pound 
and  burning  120  grains  an  hour.  An  ordinary  gas-burner  usually  gives  a 
light  equivalent  to  from  ten  to  fifteen  candles. 


164  LESSONS  IN  ASTRONOMY 

lime  light.  The  brightest  part  of  an  electric  arc-light 
comes  nearer  sunlight  in  intensity  than  anything  else  we 
know  of,  being  from  one-half  to  one-quarter  as  bright  as 
the  solar  surface  itself. 

The  sun's  disk  is  brightest  near  the  center,  but  the 
variation  is  slight  until  we  get  pretty  near  the  edge,  where 
the  light  falls  off  rapidly.  Just  at  the  sun's  limb,  the 
brightness  is  not  much  more  than  a  third  as  great  as  at  the 
center.  The  color  there  is  modified  also,  becoming  a  sort 
of  orange  red.  This  darkening  and  change  of  color  are 
due  to  the  general  absorption  of  light  by  the  lower  por- 
tions of  the  sun's  atmosphere.  According  to  Langley,  if 
this  atmosphere  were  suddenly  removed  the  surface  would 
shine  out  somewhere  from  two  to  five  times  as  brightly  as 
now,  arid  its  tint  would  become  strongly  blue,  like  the 
color  of  an  electric  arc. 

187.  The  Quantity  of  Solar  Heat ;  the  Solar  Constant.  — 
The  "  solar  constant "  is  the  number  of  heat-units  which  a 
square  unit  of  the  earth's  surface,  unprotected  by  any 
atmosphere  and  squarely  exposed  to  the  sun's  rays,  would 
receive  from  the  sun  in  a  unit  of  time.  The  heat-unit 
most  used  at  present  is  the  Calory,  which  is  the  quantity 
of  heat  required  to  raise  the  temperature  of  one  kilogram 
of  water  1°  C. ;  and  as  the  result  of  the  best  observations 
thus  far  made  (Langley's)  it  appears  that  the  Solar  Constant 
is  approximately  211of  these  calories  to  a  square  meter  in 
one  minute.  At  the  earth's  surface  a  square  meter, 
owing  to  the  absorption  of  a  large  percentage  of  heat  by 

1  The  results  of  the  Smithsonian  observations,  1902-1910,  give  the 
probable  value  of  the  solar  constant  as  19.5.  This  would  change  a  little 
the  numbers  given  in  Sees.  188  and  189. 


THE  SOLAR  CONSTANT  165 

the  air,  would,  however,  seldom  actually  receive  more  than 
from  ten  to  fifteen  calories  in  a  minute. 

The  true  value  of  the  solar  constant  is  still  uncertain  by 
a  very  large  percentage,  different  observers  giving  values 
all  the  way  from  20  to  40. 

The  method  of  determining  the  solar  constant  is  simple, 
so  far  as  the  principle  goes,  but  the  practical  difficulties 
are  serious,  and  thus  far  have  prevented  our  obtaining  the 
accuracy  desirable.  The  determination  is  made  by  allowing 
a  beam  of  sunlight  of  known  diameter  to  fall  upon  a  known 
quantity  of  water  for  a  known  time,  and  measuring  how 
much  the  water  rises  in  temperature.  The  principal  diffi- 
culty lies  in  determining  the  proper  allowance  to  be  made 
for  absorption  of  the  sun's  heat  in  passing  through  the 
air,  since  this  absorption  varies  continually  and  to  a  great 
extent  with  changing  conditions.  Besides  this  it  is  neces- 
sary to  measure  and  allow  for  the  heat  which  is  received 
by  the  water  during  the  experiment  from  other  sources 
than  the  sun. 

188.  Solar  Heat  at  the  Earth's  Surface.  —  Since  it 
requires  about  80  calories  of  heat  to  melt  one  kilogram  of 
ice,  it  follows  that,  taking  the  solar  constant  at  21,  the 
heat  received  from  the  sun  when  overhead  would  melt  in 
an  hour  a  sheet  of  ice  about  T7^  of  an  inch  thick,  From 
this  it  is  easily  computed  that  the  amount  of  heat  received 
by  the  earth  from  the  sun  in  a  year  would  melt  a  shell  of 
ice  124  feet  thick  all  over  the  earth's  surface. 

."  Solar  engines  "  have  been  constructed  within  the  last 
few  years,  in  which  the  heat  received  upon  a  large  reflector 
is  made  to  evaporate  water  in  a  suitable  boiler,  and  to  drive 
a  steam  engine.  It  is  found  that  the  heat  received  upon  a 


166  LESSONS  IN  ASTRONOMY 

reflector  ten  feet  square  can  be  made  to  give  practically 
about  one  horse-power. 

189.  Radiation  from  the  Sun's  Surface.  —  If  we  attempt 
to  estimate  the  intensity  of  the  radiation  from  the  surface  of 
the  sun  itself,  we  reach  results  which  are  simply  amazing. 
We  must  multiply  the  solar  constant  observed  at  the  earth 
by  the  square  of  the  ratio  between  the  earth's  distance 
from  the  sun  and  the  distance  of  the  sun's  surface  from 
its  own  center,  i.e.,  by  the  square  of  (a|ff  f  f  -|p-)i  or  about 
46,000  :  in  other  words,  the  amount  of  heat  emitted  in  a 
minute  by  a  square  foot  of  the  sun's  surface  is  about 
46,000  times  as  great  as  tha.t  received  by  a  square  foot  of 
surface  at  the  distance  of  the  earth.  Carrying  out  the 
figures,  we  find  that  if  the  sun  were  frozen  over  com- 
pletely to  a  depth  of  about  45  feet,  the  heat  it  emits  would 
be  sufficient  to  melt  the  ice  in  one  minute  ;  that  if  a 
bridge  of  ice  could  be  formed  from  the  earth  to  the  sun 
by  an  ice  column  2.1  miles  square,  and  if  in  some  way  the 
entire  solar  radiation  could  be  concentrated  upon  it,  it 
would  be  melted  in  one  second,  and  in  seven  more  would 
be  dissipated  in  vapor. 

Expressing  it  in  terms  of  energy,  we  find  that  the  solar 
radiation  is  nearly  100,000  horse-power  continuously 
for  each  square  meter  of  the  sun's  surface. 

So  far  as  we  can  now  see,  only  a  very  small  fraction  of  this  whole 
radiation  ever  reaches  a  resting  place.  The  earth  intercepts  about 
**inrtWTTre»  and  the  other  planets  of  the  solar  system  receive  in 
all  perhaps  from  ten  to  twenty-  times  as  much.  Something  like 
seems  to  be  utilized  within  the  limits  of  the  solar  system. 


190.    The  Sun's  Temperature.  —  We  can  determine  with 
some  accuracy  the  amount  of  heat  which  the  sun  gives  : 


THE  SUN'S  TEMPERATURE  167 

to  find  its  temperature  is  a  very  different  thing,  and  we 
really  have  very  little  knowledge  about  it,  except  that  it 
must  be  extremely  high,  —  far  higher  than  that  of  any 
terrestrial  source  of  heat  now  known.  The  difficulty  is 
that  our  laboratory  experiments  do  not  give  the  necessary 
data  from  which  we  can  determine  what  temperature  sub- 
stances like  those  of  which  the  sun  is  composed  must  have, 
in  order  to  enable  them  to  send  out  heat  at  the  rate  which 
we  observe.  Of  two  bodies  at  precisely  the  same  tempera- 
ture, one  may  send  out  heat  a  hundred  times  more  rapidly 
than  the  other. 

The  estimates  as  to  the  temperature  of  the  photosphere 
run  all  the  way  from  the  very  low  ones  of  some  of  the 
French  physicists  (who  set  it  at  about  2500°  C.)  to  the 
absurd  values  of  Secchi  and  Ericsson,  who  put  the  figure 
among  the  millions.  The  latest  and  most  authoritative 
determinations  by  Wilson  and  Gray  in  Ireland  make  it 
about  7000°  C.,  or  12,500°  F.  The  highest  terrestrial 
temperature  (attained  in  the  electric  arc)  is  about  4000°  C. 

A  very  impressive  demonstration  of  the  intensity  of  the 
sun's  heat  is  found  in  the  fact  that  in  the  focus  of  a 
powerful  burning  lens  all  known  substances  melt  and 
vaporize ;  and  yet  it  can  be  shown  that  at  the  focus  of  the 
lens  the  temperature  can  never  even  nearly  equal  that  of 
the  source  from  which  the  heat  is  derived. 

191.  Constancy  of  the  Sun's  Heat.  -  -  It  seems  now 
very  probable  that  the  amount  of  the  sun's  radiation 
varies  from  time  to  time.  'Recent  results  obtained  by 
the  Smithsonian  observers  indicate  that  the  solar  "con- 
stant" is  subject  to  fluctuations  of  from  three  to  five 
per  cent. 


168  LESSONS  IN  ASTRONOMY 

As  to  any  steady  progressive  increase  or  decrease  in  the 
amount  of  heat  received  from  the  sun,  it  is  quite  certain 
that  no  considerable  change  has  occurred  for  the  past  two 
thousand  years,  because  the  distribution  of  plants  and 
animals  on  the  earth's  surface  is  practically  the  same  as  in 
the  earliest  days  of  history.  It  is,  however,  rather  prob- 
able than  otherwise  that  the  great  changes  of  climate,  which 
Geology  indicates  as  having  formerly  taken  place  on  the 
earth,  may  ultimately  be  traced  to  changes  in  the  condition 
of  the  sun. 

192.  Maintenance  of  the  Solar  Heat.  —  We  cannot  here 
discuss  the  subject  fully,  but  must  content  ourselves  with 
saying,  - 

First,  negatively,  that  this  maintenance  cannot  be 
accounted  for  on  the  supposition  that  the  sun  is  a  hot 
body,  solid  or  liquid,  simply  cooling ,  nor  by  combustion, 
nor  (adequately)  by  the  fall  of  meteors  on  the  sun's  sur- 
face, though  this  cause  undoubtedly  operates  to  a  limited 
extent. 

Second,  we  can  say  positively,  that  the  solar  radiation  can 
be  accounted  for  on  the  hypothesis  first  proposed  by  Helm- 
holtz,  that  the  sun  is  mainly  gaseous,  and  shrinking  slowly 
but  continuously.  While  we  cannot  see  any  such  shrink- 
age, because  it  is  too  slow,  it  is  a  matter  of  demonstration 
that  if  the  sun's  diameter  should  contract  about  200  feet 
a  year,  heat  enough  would  be  generated  to  keep  up  its  radi- 
ation without  any  lowering  of  its  temperature.  If  the 
shrinkage  were  more  than  this,  the  sun  would  be  hotter  at 
the  end  of  the  year  than  it  was  at  the  beginning. 

We  can  only  say  that  while  no  other  theory  meets  the 
conditions  of  the  problem,  this  appears  to  do  so  perfectly, 


AGE  AND  DURATION  OF  SUN  169 

and  therefore  has  probability  in  its  favor.  It  seems  to  be 
only  a  continuation  of  the  process  of  condensation  by 
which  the  sun  itself  and  the  solar  system  have  been 
formed  from  the  original  cloud  or  nebula. 

193.  Age  and  Duration  of  the  Sun.  —  Of  course  if  this 
theory  is  correct,  the  sun's  heat  must  ultimately  come  to 
an  end ;  and  looking  backward,  it  must  have  had  a  begin- 
ning.    If  the  sun  keeps  up  its  present  rate  of  radiation, 
it  must,  on  this  hypothesis,  shrink  to  about  half  its  diam- 
eter in  some  5,000000  years  at  the  longest.     It  will  then  be 
eight  times  as  dense  as  now,  and  can  hardly  continue  to  be 
mainly  gaseous,  so  that  the  temperature  must  begin  to  fall 
quite  sensibly.     It  is  not,  therefore,  likely,  in  the  opinion 
of  Professor  Newcomb,  that  the  sun  will  continue  to  give 
heat  sufficient  to  support  the  present  conditions  upon  the 
earth  for  much  more  than  10,000000  years,  if  so  long. 

On  the  other  hand,  it  is  certain  that  the  shrinkage  of  the 
sun  to  its  present  dimensions  from  a  diameter  larger  than 
that  of  the  orbit  of  Neptune,  the  remotest  of  the  planets, 
would  produce  about  18,000000  times  as  much  heat  as 
the  sun  now  throws  out  in  a  year.  Hence,  if  the  sun's  heat 
has  been,  and  still  is,  wholly  due  to  the  contraction  of  its 
mass,  it  cannot  have  been  emitting  heat  at  the  present  rate, 
on  this  shrinkage  hypothesis,  for  more  than  18,000000 
years.  But  notice  the  "  (£"  It  is  quite  possible  that  a 
part  of  the  solar  radiation  may  be  due  to  radium  and 
other  radioactive  substances.  If  so,  the  solar  system  may 
be  much  older. 

194.  Constitution  of  the  Sun.  —  To  sum  up :  the  received 
opinion  is  that  the  sun  is  mainly  composed  of  the  same 
chemical  elements  as  the  earth,  but  that  in  the  body,  or 


170  LESSONS  IN  ASTRONOMY 

nucleus,  of  the  sun  the  heat  is  so  tremendous  that  they  are 
all  in  the  state  of  vapor  or  gas  in  spite  of  the  great  pressure 
to  which  they  are  subjected. 

The  photosphere  is  probably  a  sheet  of  luminous  clouds, 
constituted  mechanically  like  terrestrial  clouds,  i.e.,  of 
small,  solid,  or  liquid  particles,  very  likely  of  carbon, 
floating  in  gas. 

These  photospheric  clouds  float  in  an  atmosphere  com- 
posed of  those  gases  which  do  not  condense  into  solid  or 
liquid  particles  at  the  temperature  of  the  solar  surface. 
This  atmosphere  is  laden,  of  course,  with  the  vapors  out 
of  which  the  clouds  have  been  condensed,  and  constitutes 
the  reversing  layer  which  produces  the  dark  lines  of  the 
solar  spectrum. 

The  chromosphere  and  prominences  appear  to  be  com- 
posed of  permanent  gases,  mainly  hydrogen  and  helium, 
which  are  mingled  with  the  vapors  in  the  region  of  the 
photosphere,  but  rise  to  far  greater  elevations.  For  the 
most  part  the  prominences  appear  to  be  formed  by  jets  of 
hydrogen  and  helium,  ascending  through  the  interstices 
between  the  photospheric  clouds,  like  flames  playing  over 
a  coal  fire. 

As  to  the  corona,  it  is  as  yet  impossible  to  give  any 
satisfactory  explanation  of  all  the  phenomena  that  it  pre- 
sents, and  since  thus  far  it  has  been  possible  to  observe  it 
only  during  the  brief  moments  of  total  eclipses,  progress 
in  its  study  has  been  necessarily  slow. 


CHAPTER  VII 

ECLIPSES  AND  THE  TIDES 

Form  and  Dimensions  of  Shadows  —  Eclipses  of  the  Moon  —  Solar  Eclipses  — 
Total,  Annular,  and  Partial  —  Number  of  Eclipses  in  a  Year  —  Recurrence 
of  Eclipses  and  the  Saros  —  Occupations  —  The  Tides 

195.  Occasionally  the  sun  or  moon  is  for  a  short  time 
obscured  by  an  Eclipse  (literally,  a  "swoon").  Solar 
eclipses,  when  total,  are  among  the  most  impressive  phe- 
nomena in  the  range  of  human  experience,  and  find  place 
all  along  the  records  of  authentic  history.  To  the  super- 
stitious and  ignorant  they  have  always  been  terrifying  and 
portentous;  but  to  the  astronomer  wonderfully  beautiful 
—  golden  opportunities  for  observations  important  and 
otherwise  impossible. 

An  eclipse  of  the  moon  is  caused  by  its  passing  through 
the  shadow  of  the  earth;  an  eclipse  of  the  sun  by  the 
moon's  passing  between  the  sun  and  the  observer,  or,  what 
comes  to  the  same  thing,  by  the  passage  of  the  moon's 
shadow  over  the  observer. 

The  "shadow,"  in  Astronomy,  is  the  space  from  which 
sunlight  is  excluded  by  an  intervening  body ;  speaking 
geometrically,  it  is  a  solid,  not  a  surface.  Since  the  sun 
and  the  other  heavenly  bodies  are  very  nearly  spherical,  these 
shadows  are  cones  with  their  axes  in  the  line  which  joins  the 
centers  of  the  sun  and  the  shadow-casting  body,  the  point 
being  always  directed  away  from  the  sun. 

171 


172 


LESSONS  IN  ASTRONOMY 


ECLIPSES  OF  THE  MOON 

196.  Dimensions  of  the  Earth's  Shadow.  —  The  length 
of  the  shadow  is  easily  found.  In  Fig.  44,0  is  the  center 
of  the  sun  and  E  the  center  of  the  earth,  and  aCb  is  the 
shadow  of  the  earth  cast  by  the  sun.  It  is  readily  shown 
by  Geometry  that  if  we  call  EC,  the  length  of  the  shadow, 
L,  and  OE,  the  distance  of  the  earth  from  the  sun,  Z>,  then 

L  =  D  x  (      _    J »  R  being  OA,  the  radius  of  the  sun,  and  r 
being  Ea,  the  radius  of  the  earth.     Putting  in  the  values  of 


FIG.  44.  — The  Earth's  Shadow 


R  and  r  from  Sees.  160  and  112  (where,  however,  the  earth's 
mean  diameter  is  given  instead  of  radius)   the  fraction, 

/     r     \  1 

(      _     J  i  comes  out  nearly  T77o~r  >  and  multiplying  this 

by  D  (93,000000),  we  get  857,000  miles  for  the  average 
length  of  the  earth's  shadow. 

The  length  varies  about  14,000  miles  on  each  side  of 
the  mean,  in  consequence  of  the  variation  of  the  earth's 
distance  from  the  sun  at  different  times  of  the  year. 

From  the  cone  aCb  all  sunlight  is  excluded,  or  would  be  were  it 
not  for  the  fact  that  the  atmosphere  of  the  earth  bends  some  of  the 


LUNAE  ECLIPSES  173 

rays  which  pass  near  the  earth's  surface  into  its  shadow.  The  effect 
of  this  atmospheric  refraction  is  to  increase  the  apparent  diameter 
of  the  shadow  about  two  per  cent,  but  to  make  it  less  perfectly  dark. 

If  we  draw  the  lines  Be  and  Ad,  crossing  at  P,  between 
the  earth  and  the  sun,  they  will  bound  the  penumbra, 
within  which  a  part,  but  not  the  whole,  of  the  sunlight  is 
cut  off ;  an  observer  outside  of  the  shadow,  but  within  this 
partly  shaded  space,  would  see  the  earth  as  a  black  body 
encroaching  on  the  sun's  disk,  though  not  covering  it. 

197.  Lunar  Eclipses.  —  The  axis,  or  central  line,  of  the 
earth's  shadow  is  always  directed  to  a  point  directly  oppo- 
site the  sun.  If,  then,  at  the  time  of  full  moon,  the  moon 
happens  to  be  near  the  ecliptic,  i.e.,  not  far  from  one  of 
the  nodes  (the  points  where  her  orbit  cuts  the  ecliptic), 
she  will  pass  through  the  shadow  and  be  eclipsed.  Since, 
however,  the  moon's  orbit  is  inclined  5°  8'  to  the  ecliptic, 
lunar  eclipses  do  not  happen  very  frequently, — seldom  more 
than  twice  a  year,  because  the  moon  at  the  full  usually 
passes  north  or  south  of  the  shadow,  without  touching  it. 

Lunar  eclipses  are  of  two  kinds,  partial  and  total :  total 
when  she  passes  completely  into  the  shadow ;  partial  when 
she  only  partly  enters  it,  going  so  far  to  the  north  or  south 
of  the  center  that  only  a  portion  of  the  disk  is  obscured. 
An  eclipse  of  the  moon  when  central  (i.e.,  when  the  moon 
crosses  the  center  of  the  shadow)  may  continue  total  for 
about  two  hours,  the  interval  from  the  first  to  the  last 
contact  being  about  two  hours  more.  This  depends  upon 
the  facts  that  the  moon's  hourly  motion  is  nearly  equal  to 
its  own  diameter,  and  that  the  diameter  of  the  earth's 
shadow  where  the  moon  crosses  it  is  between  two  and 
three  times  the  diameter  of  the  moon  itself.  The  duration 


174  LESSONS  IN  ASTKONOMY 

of  an  eclipse  that  is  not  central  varies  of  course  with  the 
part  of  the  shadow  traversed  by  the  moon. 

198.  Phenomena  of  Total  Eclipses  of  the  Moon.  —  Half 
an  hour  or  so  before  the  moon  reaches  the  shadow,  its  edge 
begins  to  be  sensibly  darkened  by  the  penumbra,  and  the 
edge  of  the  shadow  itself,  when  it  first  touches  the  moon, 
appears  nearly  black  by  contrast  with  the  bright  parts  of 
the  moon's  surface.  To  the  naked  eye  the  outline  of  the 
shadow  looks  fairly  sharp ;  but  even  with  a  small  telescope 
it  appears  indefinite,  and  with  a  large  telescope  of  high 
magnifying  power  the  edge  of  the  shadow  becomes  entirely 


A' 
FIG.  45.  — Light  bent  into  Earth's  Shadow  by  Refraction 

indistinguishable,  so  that  it  is  impossible  to  determine 
within  half  a  minute  or  so  the  time  when  it  reaches  any 
particular  point. 

After  the  moon  has  wholly  entered  the  shadow,  her  disk 
is  usually  distinctly  visible,  illuminated  with  a  dull,  copper- 
colored  light,  which  is  sunlight,  deflected  around  the  earth 
into  the  shadow  by  the  refraction  of  our  atmosphere,  as 
illustrated  by  Fig.  45.  The  brightness  of  the  moon's  disk 
during  a  total  eclipse  of  the  moon  differs  greatly  at  dif- 
ferent times,  according  to  the  condition  of  the  weather  on 
the  parts  of  the  earth  which  happen  to  lie  at  the  edges  of 
the  earth's  disk  as  seen  from  the  moon.  If  it  is  cloudy 
and  stormy  there,  little  light  will  reach  the  moon  ;  if  it 
happens  to  be  clear,  the  quantity  of  light  deflected  into 


DIMENSIONS  OF  MOON'S  SHADOW  175 

the  shadow  may  be  very  considerable.  In  the  lunar  eclipse 
of  1884,  the  moon  was  for  a  time  absolutely  invisible  to 
the  naked  eye,  —  a  very  unusual  circumstance. 

During  the  eclipse  of  Jan.  28,  1888,  although  the  moon  was 
pretty  bright  to  the  eye,  Pickering  found  that  its  photographic  power, 
when  centrally  eclipsed,  was  only  about  TCT$irro  °f  what  it  had  been 
before  the  shadow  covered  it. 

199.  Computation  of  a  Lunar  Eclipse.  —  The  computation  of  a 
lunar  eclipse  is  not  at  all  complicated,  though  we  do  not  propose  to 
enter  into  it.  Since  all  its  phases  are  seen  everywhere  at  the  same 
absolute  instant  wherever  the  moon  is  above  the  horizon,  it  follows 
that  a  single  calculation  giving  the  Greenwich  times  of  the  different 
phenomena  is  all  that  is  needed.  Such  computations  are  made  and 
published  in  the  Nautical  Almanac.  The  observer  needs  only  to  cor- 
rect  the  predicted  time  by  simply  adding  or  subtracting  his  longitude 
from  Greenwich,  in  order  to  get  the  true  local  time.  With  an  eclipse 
of  the  sun  the  case  is  very  different. 


ECLIPSES   OF   THE   SUN 

200.  The  Length  of  the  Moon's  Shadow  is  very  nearly 
?1_  of  its  distance  from  the  sun,  and  averages  232,150 
miles.  It  varies  not  quite  7800  miles,  ranging  from 
228,300  to  236,050. 

Since  the  mean  length  of  the  shadow  is  less  than  the 
mean  distance  from  the  earth  (238,800  miles),  it  is  evident 
that  on  the  average  the  shadow  will  fall  short  of  the  earth. 
The  eccentricity  of  the  moon's  orbit,  however,  is  so  great 
that  she  is  sometimes  more  than  31,000  miles  nearer  than 
at  others.  If  when  the  moon  is  nearest  the  earth,  the 
shadow  happens  to  have  at  the  same  time  its  greatest  pos- 
sible length,  its  point  may  reach  nearly  18,400  miles  beyond 


176  LESSORS  IX  ASTRONOMY 

the  earth's  surface.  In  this  case  the  cross-section  of  the 
shadow  where  the  earth's  surface  cuts  it  (at  o  in  Fig.  46) 
will  be  about  168  miles  in  diameter,*  which  is  the  largest 
value  possible.  On  the  other  hand,  when  the  moon  is 
farthest  from  the  earth,  we  may  have  the  state  of  things 
indicated  by  placing  the  earth  at  B  in  Fig.  44.  The  ver- 
tex of  the  shadow,  V,  will  then  fall  about  21,000  miles  short 
of  the  earth's  surface,  and  the  cross-section  of  the  shadow 
produced  will  have  a  diameter  of  196  miles  at  0',  where 
the  earth's  surface  cuts  it. 

201,  Total  and  Annular  Eclipses.  —  To  an  observer  within 
the  shadow  cone  (i.e.,  between  V  and  the  moon,  Fig.  46) 
the  sun  will  be  totally  eclipsed.  An  observer  in  the 

fe 

To  Sun 
FIG.  46.  — The  Moon's  Shadow  on  the  Earth 

"produced"  cone  beyond  Twill  see  the  moon  apparently 
smaller  than  the  sun,  leaving  a  ring  of  the  sun  uneclipsed ; 
this  is  what  is  called  an  annular  eclipse.  These  annular 
eclipses  are  considerably  more  frequent  than  the  total,  and 
now  and  then  an  eclipse  is  annular  in  part  of  its  course 
across  the  earth  and  total  in  part.  This  is  when  the  point 
of  the  moon's  shadow  extends  beyond  the  surface  of  the 
earth,  but  does  not  reach  as  far  as  its  center. 

The  track  of  the  eclipse  across  the  earth  will,  of  course,  be 
a  narrow  stripe  having  its  width  equal  to  the  cross-section 
of  the  shadow,  and  extending  across  the  hemisphere  which 
is  turned  towards  the  moon  at  the  time,  though  not 


PENUMBRA  AND  PARTIAL  ECLIPSES  177 

necessarily  passing  the  center  of  that  hemisphere.  Its 
course  is  always  from  the  west  towards  the  east,  but 
usually  considerably  inclined  towards  the  north  or  south. 

202.  The  Penumbra  and  Partial  Eclipses. — The  penumbra 
can  easily  be  shown  to  have  a  diameter  on  the  line   CI> 
(Fig.  46)  a  little  more  than  twice  the  diameter  of  the  moon, 
or  over  4000   miles.      An  observer  situated  within  this 
penumbra  has  a  partial  eclipse.     If  he  is  near  to  the  cone 
of  the  shadow,  the  sun  will  be  mostly  covered  by  the  moon  ; 
if  near  the  outer  edge  of  the  penumbra,  the  moon  will  but 
slightly  encroach  on  the  sun's  disk.     While,  therefore,  a 
total  or  annular  eclipse  is  visible  as  such  only  by  observers 
within  the  narrow  path  traversed  by  the  shadow-spot,  the 
same  eclipse  will  be  visible  as  a  partial  one  anywhere  within 
2000  miles  on  each  side  of  the  path;  and  the  2000  miles 
must  be  reckoned  square  to  the  axis  of  the  shadow,  and 
may  correspond   to   a   much   greater   distance  upon  the 
spherical  surface  of  the  earth. 

203.  Velocity  of  the  Shadow  and  Duration  of  an  Eclipse.  — 
Were  it  not  for  the  earth's  rotation,  the  moon's  shadow 
would  pass  the  observer  at  the  rate  of  about  2100  miles  an 
hour.     The  earth,  however,  is  rotating  towards  the  east  in 
the  same  general  direction  as  that  in  which  the  shadow 
moves,  so  that  the  relative  velocity  is  usually  much  less. 

A  total  eclipse  of  the  sun  observed  at  a  station  near  the 
equator,  under  the  most  favorable  conditions  possible,  may 
continue  total  for  about  7m58s.  In  latitude  40°  the  duration 
can  barely  equal  6m158. 

An  annular  eclipse  may  last  at  the  equator  for  12m248, 
the  maximum  width  of  the  ring  of  the  sun  visible  around 
the  moon  being  V  37". 


178  LESSONS  IN  ASTRONOMY 

In  the  observation  of  an  eclipse,  four  contacts  are  recognized:  the 
first  when  the  edge  of  the  moon  first  touches  the  edge  of  the  sun, 
the  second  when  the  eclipse  becomes  total  or  annular,  the  third  at 
the  cessation  of  the  total  or  annular  phase,  and  the  fourth  when  the 
moon  finally  leaves  the  solar  disk.  ^From  the  first  contact  to  the 
fourth  the  time  may  be  a  little  over  four  hours.  In  a  partial  eclipse, 
only  the  first  and  fourth  are  observable,  and  the  interval  between  them 
may  be  very  small  when  the  moon  just  grazes  the  edge  of  the  sun. 

The  magnitude  of  an  eclipse  is  usually  reckoned  in  digits,  the 
digit  being  TV  of  the  sun's  diameter.  An  eclipse  of  nine  digits  is 
one  in  which  the  disk  of  the  moon  covers  three-fourths  of  the  sun's 
diameter  at  the  middle  of  the  eclipse. 

204.  Phenomena  of  a  Solar  Eclipse.  —  There  is  nothing 
of  special  interest  until  the  sun  is  mostly  covered,  though 
before  that  time  the  shadows  cast  by  the  foliage  begin  to  be 
peculiar. 

The  light  shining  through  every  small  interstice  among  the  leaves, 
instead  of  forming  as  usual  a  circle  on  the  ground,  makes  a  little 
crescent,  —  an  image  of  the  partly  covered  sun. 

About  ten  minutes  before  totality  the  darkness  begins  to 
be  felt,  and  the  remaining  light,  coming,  as  it  does,  from  the 
edge  of  the  sun,  is  not  only  faint  but  yellowish,  more  like 
that  of  a  calcium  light  than  sunshine.  Animals  are  per- 
plexed, and  birds  go  to  roost.  The  temperature  falls,  and 
dew  appears.  In  a  few  moments,  if  the  observer  is  so  situ- 
ated that  his  view  commands  the  distant  western  horizon, 
the  moon's  shadow  is  seen  coming,  much  like  a  heavy 
thunder-shower,  and  advancing  with  almost  terrifying 
swiftness.  As  soon  as  the  shadow  arrives,  and  sometimes 
a  little  before,  the  corona  and  prominences  become  visible, 
while  the  brighter  planets  and  stars  of  the  first  three 
magnitudes  make  their  appearance. 


FREQUENCY  OF  ECLIPSES  179 

The  suddenness  with  which  the  darkness  pounces  upon 
the  observer  is  startling.  The  sun  is  so  brilliant  that  even 
the  small  portion  which  remains  visible  up  to  the  moment 
of  total  obscuration  so  dazzles  the  eye  that  it  is  unprepared 
for  the  sudden  transition.  In  a  few  moments,  however,  the 
eye  adjusts  itself,  and  it  is  found  that  the  darkness  is  really 
not  very  intense.  If  the  totality  is  of  short  duration,  say 
not  more  than  two  minutes,  there  is  not  much  difficulty  in 
reading  an  ordinary  watch  face.  In  an  eclipse  of  long 
duration  (four  or  five  minutes)  it  is  much  darker,  and 
lanterns  become  necessary. 

205.  Calculation  of  a  Solar  Eclipse.  —  A  solar  eclipse  cannot  be 
dealt  with  in  any  such  summary  way  as  a  lunar  eclipse,  because  the 
absolute  times  of  contact  are  different  at  every  different  station.    The 
path  which  the  shadow  of  a  total  eclipse  will  describe  upon  the  earth 
is  roughly  mapped  out  in  the  Nautical  Almanacs  several  years  before- 
hand, and  with  the  chart  are  published  the  data  necessary  to  enable 
one  to  calculate  with  accuracy  the  phenomena  for  any  given  place  ; 
but  the  computation  is  rather  long  and  somewhat  complicated. 

Th.  Oppolzer,  a  Viennese  astronomer,  published  some  years  ago  a 
remarkable  book  entitled  "  The  Canon  of  Eclipses,"  containing  the 
elements  of  all  eclipses  (8000  solar  and  5200  lunar)  occurring  between 
the  year  1207  B.C.  and  A.D.  2162,  with  maps  showing  the  approximate 
tracks  of  all  the  solar  eclipses. 

206.  Frequency  of  Eclipses  and  Number  in  a  Year.  —  The 

least  possible  number  in  a  year  is  two,  both  of  the  sun ;  the 
largest  seven,  five  solar  and  two  lunar  or  fpur  solar  and 
three  lunar;  the  most  usual  number  is  four. 

The  eclipses  of  a  given  year  always  take  place  at  two 
opposite  seasons,  which  may  be  called  the  eclipse  months 
of  the  year,  near  the  times  when  the  sun  crosses  the  nodes  of 
the  moon's  orbit.  Since  the  nodes  move  westward  around 


180  LESSONS  IN  ASTRONOMY 

the  ecliptic  once  in  about  nineteen  years  (Sec.  134),  the 
time  occupied  by  the  sun  in  passing  from  a  node  to  the 
same  node  again  is  only  346.62  days,  which  is  sometimes 
called  the  eclipse  year. 

Taking  the  whole  earth  into  account,  the  solar  eclipses 
are  the  more  numerous,  nearly  in  the  ratio  of  3 :  2.  It  is 
not  so,  however,  with  those  which  are  visible  at  a  given  place. 
A  solar  eclipse  can  be  seen  only  by  persons  who  happen 
to  be  on  the  narrow  track  described  by  the  moon's  shadow 
in  its  passage  across  the  globe,  while  a  lunar  eclipse  is 
visible  over  considerably  more  than  half  the  earth,  —  either 
at  its  beginning  or  end,  if  not  throughout  its  whole  duration. 
This  more  than  reverses  the  proportion,  i.e.,  at  any  given 
place  lunar  eclipses  are  considerably  more  frequent  than 
solar.  Solar  eclipses  that  are  total  somewhere  or  other  on 
the  earth's  surface  are  not  very  rare,  averaging  about  one  for 
every  year  and  a  half.  But  at  any  given  place  a  total  eclipse 
happens  only  once  in  about  360  years  in  the  long  run. 

During  the  19th  century  seven  shadow  tracks  crossed  the  United 
States,  the  last  in  May,  1900.  During  the  20th  the  same  number 
are  predicted,  —  the  next  in  1918,  the  track  of  which  runs  from 
Oregon  to  Florida.  (Our  insular  possessions  are  not  included  in 
this  reckoning.) 

207.  Recurrence  of  Eclipses ;  the  Saros.  —  It  was  known 
to  the  Egyptians,  even  in  prehistoric  times,  that  eclipses 
occur  at  regular  intervals  of  18  years  and  11 J  days  (10^ 
days,  if  there  happen  to  be  five  leap  years  in  the  interval). 
They  named  this  period  the  Saros.  It  consists  of  223  syn- 
odic months,  containing  6585.32  days,  while  19  eclipse  years 
contain  6585.78.  The  difference  is  only  about  11  hours,  in 
which  time  the  sun  moves  on  the  ecliptic  about  28'. 


CAUSE  OF  THE  TIDES  181 

If,  therefore,  a  solar  eclipse  should  occur  to-day  with 
the  sun  exactly  at  one  of  the  moon's  nodes,  at  the  end  of 
223  months  the  new  moon  will  find  the  sun  again  close  to 
the  node  (only  28'  west  of  it),  and  a  very  similar  eclipse 
will  occur  again ;  but  the  track  of  this  new  eclipse  will  lie 
about  8  hours  of  longitude  farther  west  on  the  earth,  on 
account  of  the  odd  -^  of  a  day  in  the  Saros.  The  usual 
number  of  eclipses  in  a  Saros  is  a  little  over  70,  varying 
two  or  three  one  way  or  the  other. 

In  the  Saros  closing  Dec.  22,  1889,  the  total  number  was  72, — 
29  lunar  and  43  solar.  Of  the  latter,  29  were  central  (13  total,  16 
annular),  and  14  were  only  partial. 

THE  TIDES 

208.  Cause  of  the  Tides.  —  Since  the  tides  depend  upon 
the  action  of  the  sun  and  of  the  moon  upon  the  waters  of 
the  earth,  they  may  properly 
be  considered  here  before  we 
deal  with  the  planetary  sys- 
tem. We  do  not  propose  to  B- 
go  into  the  mathematical 
theory  of  the  phenomena  at 
all,  as  it  lies  far  beyond  our  E 

v     .,    ,.  ,  FIG.  47.  —  The  Tides 

limitations ;  but  any  person 

can  see  that  a  liquid  globe  falling  freely  towards  an  attract- 
ing body,  which  attracts  the  nearer  portions  more  powerfully 
than  the  more  remote,  will  be  drawn  out  into  an  elongated 
lemon-shaped  form,  as  illustrated  in  Fig.  47,  and  if  the 
globe,  instead  of  being  liquid,  be  mainly  solid,  but  has 
large  quantities  of  liquid  on  its  surface,  substantially  the 


182  LESSONS  IN  ASTRONOMY 

same  result  will  follow.  Now  the  earth  is  free  in  space,  and 
though  it  has  other  motions,  it  is  also  falling  towards  the 
moon  and  towards  the  sun,  and  is  affected  precisely  as  it 
would  be  if  its  other  motions  did  not  exist.  The  conse- 
quence is  that  at  any  time  there  is  a  tendency  to  elongate 
those  diameters  of  the  earth  which  are  pointed  towards  the 
moon  and  towards  the  sun.  The  sun  is  so  much  farther 
away  than  the  moon  that  its  effect  in  thus  deforming  the 
surface  of  the  earth  is  only  about  five-elevenths  as  great 
as  that  of  the  moon. 

209.  The  tides  consist  in  a  regular  rise  and  fall  of  the  ocean 
surface,  the  average  interval  between  corresponding  high 
waters  on  successive  days  at  any  given  place  being  24h51m, 
which  is  precisely  the  same  as  the  average  interval  between 
two  successive  passages  of  the  moon  across  the  meridian ; 
and  since  this  coincidence  is  maintained  indefinitely,  it  of 
itself  makes  it  certain  that  there  must  be  some  causal  con- 
nection between  the  moon  and  the  tides.     Some  one  has  said 
that  the  odd  fifty-one  minutes  is  the  moon's  "  earmark." 

That  the  moon  is  largely  responsible  for  the  tides  is  also 
shown  by  the  fact  that  when  the  moon  is  in  perigee,  at  the 
nearest  point  to  the  earth,  the  tides  are  nearly  twenty  per 
cent  higher  than  when  she  is  in  apogee. 

210.  Definitions.  —  While  the  water  is  rising,  it  is  flood- 
tide ;  while  falling,  it  is  ebb-tide.     It  is  high  water  at  the 
moment  when  the  water-level  is  highest,  and  low  water 
when  it  is  lowest.     The  spring-tides  are  the  largest  tides 
of  the  month,  which  occur  near  the  times  of  new  and  full 
moon,  while  the  neap  tides  are  the  smallest,  and  occur  at 
half-moon,  the  relative  heights  of  spring  and  neap  tides 
being  about  as  8  :  3  (11  +  5  : 11  -  5). 


MOTION  OF  THE  TIDES  183 

At  the  time  of  the  spring-tides,  the  interval  between 
the  corresponding  tides  of  successive  days  is  less  than  the 
average,  being  only  about  24h38m  (instead  of  24h51m),  and 
then  the  tides  are  said  to  prime.  At  the  neap  tides  the 
interval  is  greater  than  the  mean,  —  about  25h6m,  —  and 
the  tide  lags. 

The  establishment  of  a  port  is  the  mean  interval  between 
the  time  of  high  water  at  that  port  and  the  next  preceding 
passage  of  the  moon  across  the  meridian.  The  "  establish- 
ment" of  New  York,  for  instance,  is  8h13m.  The  actual 
interval  between  the  moon's  transit  and  high  water  varies, 
however,  nearly  half  an  hour  on  each  side  of  this  mean 
value  at  different  times  of  the  month,  and  under  varying 
conditions  of  the  weather. 

211.  Motion  of  the  Tides.  —  If  the  earth  were  wholly 
composed  of  water,  and  if  it  kept  always  the  same  face 
towards  the  moon,  as  the  moon  does  towards  the  earth, 
then  (leaving  out  of  account  the  sun's  action  for  the 
present)  a  permanent  tide  would  be  raised  upon  the  earth, 
as  indicated  in  Fig.  47.  The  difference  between  the  water- 
level  at  A  and  D  would  be  a  little  less  than  two  feet. 

Suppose,  now,  the  earth  put  in  rotation.  It  is  evident 
that  the  two  tidal  waves  A  and  B  would  move  over  the 
earth's  surface,  following  the  moon  at  a  certain  angle 
dependent  on  the  inertia  of  the  water,  and  tending  to 
move  with  a  westward  velocity  equal  to  the  earth's  east- 
ward rotation,  —  about  1000  miles  an  hour  at  the  equator. 
The  sun's  action  would  produce  similar  tides  superposed 
upon  the  moon's  tide,  and  about  five-elevenths  as  large ;  and 
at  different  times  of  the  month  these  two  pairs  of  tides 
would  sometimes  conspire  and  sometimes  be  opposed. 


184  LESSONS  IN  ASTRONOMY 

If  the  earth  were  entirely  covered  with  deep  water,  then, 
according  to  Professor  Darwin,  and  considering  only  the 
lunar  tide,  the  tide-waves  would  run  around  the  globe 
regularly,  and  if  the  depth  of  the  water  were  not  less  than 
14  miles,  the  two  tide  crests  would  keep  on  the  line  joining 
the  centers  of  the  moon  and  earth. 

If  the  depth  were  somewhat  less,  the  tide  crests  on  the 
equator  would  follow  the  moon  at  an  angle  of  90°,  but  in 
the  high  latitudes  they  would  still  move  as  in  the  deeper 
ocean,  while  in  some  intermediate  latitude  there  would 
be  a  belt  of  eddying  currents  without  either  rise  or  fall. 

But  the  varying  depth  of  the  ocean  in  different  regions 
and  the  irregular  contour  of  its  shore-line  greatly  compli- 
cate the  problem.  Moreover,  the  continents  of  North  and 
South  America,  with  the  southern  Antarctic  continent, 
make  a  barrier  almost  from  pole  to  pole,  leaving  only  a 
narrow  passage  at  Cape  Horn. 

As  a  consequence  it  is  quite  impossible  to  determine  by 
theory  what  the  course  and  character  of  tide-waves  must 
be.  We  have  to  depend  upon  observations,  and  observa- 
tions are  more  or  less  inadequate,  because,  with  the  excep- 
tion of  a  few  islands,  our  only  possible  tide  stations  are 
on  the  shores  of  continents  where  local  circumstances 
largely  control  the  phenomena. 

212.  Free  and  Forced  Oscillations.  —  If  the  water  of  the 
ocean  is  suddenly  disturbed,  as,  for  instance,  by  an  earth- 
quake, and  then  left  to  itself,  a  "  free  wave  "  is  formed, 
which,  if  the  horizontal  dimensions  of  the  wave  are  large 
as  compared  with  the  depth  of  the  water  (i.e.,  if  it  is  many 
hundred  miles  in  length),  will  travel  at  a  rate  which  depends 
simply  on  the  depth  of  the  water. 


COURSE  OF  THE  TIDE-WAVE  185 

Its  velocity  is  equal,  as  can  be  proved,  to  the  velocity  acquired  by 
a  body  in  falling  through  half  the  depth  of  the  ocean.  Observations 
upon  waves  caused  by  certain  earthquakes  in  South  America  and 
.Japan  have  thus  informed  us  that  between  the  coasts  of  those 
countries  the  Pacific  averages  between  2|  and  3  miles  in  depth. 

Now,  as  the  moon  in  its  apparent  diurnal  motion  passes 
across  the  American  continent  each  day  and  comes  over 
the  Pacific  Ocean,  it  starts  such  a  "  parent "  wave  in  the 
Pacific,  and  a  second  one  is  produced  twelve  hours  later. 
And  in  the  same  manner  the  sun,  of  course,  also  starts  its 
own  independent  smaller  tide-waves. 

These  waves,  once  started,  move  on  nearly  (but  not 
exactly)  like  a  free  earthquake  wave  —  not  exactly,  because 
the  velocity  of  the  earth's  rotation  being  about  1040  miles 
at  the  equator,  the  moon  moves  (relatively)  westward 
faster  than  the  wave  can  naturally  follow  it,  and  so  for 
a  while  the  moon  slightly  accelerates  the  wave.  The  tidal 
wave  is  thus,  in  its  origin,  a  "forced  oscillation";  in  its 
subsequent  travel  it  is  very  nearly,  but  not  entirely,  "  free." 

Of  course  as  the  moon  passes  on  over  the  Indian  and 
Atlantic  oceans,  it  starts  waves  in  them  also,  which  com- 
bine with  the  parent  wave  coming  in  from  the  Pacific. 

213,  Course  of  Travel  of  the  Tide- Wave. — The  parent  wave 
appears  to  start  twice  a  day  in  the  Pacific  Ocean,  off  Callao,  on  the 
coast  of  South  America.  From  this  point  the  wave  travels  northwest 
through  the  deep  water  of  the  Pacific  at  the  rate  of  about  850  miles 
an  hour,  reaching  Kamchatka  in  ten  hours.  Through  the  shallow 
water  to  the  west  and  southwest  the  velocity  is  only  from  400  to  600 
miles  an  hour,  so  that  the  wave  is  six  hours  old  when  it  reaches  New 
Zealand.  Passing  on  by  Australia  and  combining  with  the  small 
wave  which  the  moon  starts  in  the  Indian  Ocean,  the  resultant  tide 
crest  reaches  the  Cape  of  Good  Hope  in  about  twenty-nine  hours  and 


186  LESSONS  IN  ASTRONOMY 

enters  the  Atlantic.  Here  it  combines  with  a  smaller  tide-wave, 
twelve  hours  younger,  which  has  "  backed  "  into  the  Atlantic  around 
Cape  Horn,  and  it  is  also  modified  by  the  direct  tide  produced  by  the 
moon  and  sun  in  the  Atlantic.  The  tide  resulting  from  the  com- 
bination of  these  waves  then  travels  northward  through  the  Atlantic 
at  the  rate  of  about  700  miles  an  hour.  It  is  about  forty  hours  old 
when  it  first  reaches  the  coast  of  the  United  States  in  Florida ;  and 
our  coast  lies  in  such  a  direction  that  it  arrives  at  all  the  principal 
ports  within  two  or  three  hours  of  the  same  time.  It  is  forty-one  or 
forty-two  hours  old  when  it  reaches  New  York  and  Boston. 

To  reach  London  it  has  to  travel  around  the  northern  end  of 
Scotland  and  through  the  North  Sea,  and  is  nearly  sixty  hours  old 
when  it  arrives  at  that  port. 

In  the  great  oceans  there  are  three  or  four  such  tide  crests,  follow- 
ing nearly  in  the  same  track,  but  with  continual  minor  changes. 

214.  Height  of  the  Tides.  —  In  mid  ocean  the  difference 
between  high  and  low  water  is  usually  between  two  and 

•^  ^ ^  ^-^  ^^*  A  r 

B  ^w     F   y  y 

FIG.  48.  — Increase  in  Height  of  Tide  on  approaching  the  Shore 

three  feet,  as  observed  on  isolated  islands  in  the  deep  water. 
On  the  continental  shores  the  height  is  ordinarily  much 
greater.  As  soon  as  the  tide-wave  "touches  bottom,"  so 
to  speak,  the  velocity  is  diminished,  the  tide  crests  are 
crowded  more  closely  together,  and  the  height  of  the  tide 
is  very  much  increased,  as  indicated  in  Fig.  48. 

Theoretically,  it  varies  inversely  as  the  fourth  root  of  the  depth ; 
i.e.,  where  the  water  is  100  feet  deep  the  tide-wave  should  be  twice 
as  high  as  at  the  depth  of  1600  feet. 


TIDES  IN  RIVERS  187 

Where  the  configuration  of  the  shore  forces  the  tide  into 
a  corner  it  sometimes  rises  very  high.  At  Minas  Basin,  on 
the  Bay  of  Fundy,  tides  of  70  feet  are  reported  as  not 
uncommon,  and  an  altitude  of  100  feet  is  said  to  occur 
sometimes.  At  Bristol,  in  the  English  Channel,  tides  of 
40  or  50  feet  are  reached ;  at  the  same  time,  on  the  coast 
of  Ireland,  just  opposite,  the  tide  is  very  small. 

215.  Tides  in  Rivers.  —  The  tide-wave  ascends  a  river  at  a  rate 
which  depends  upon  the  depth  of  the  water,  the  amount  of  friction, 
and  the  swiftness  of  the  stream.  It  may,  and  generally  does,  ascend 
until  it  comes  to  a  rapid  where  the  velocity  of  the  current  is  greater 
than  that  of  the  wave.  In  shallow  streams,  however,  it  dies  out 
earlier.  Contrary  to  what  is  usually  supposed,  it  often  ascends  to  an 
elevation  far  above  that  of  the  highest  crest  of  the  tide-wave  at  the 
river's  mouth.  In  the  La  Plata  and  Amazon,  the  tide  goes  up  to  an 
elevation  of  at  least  100  feet  above  the  sea-level.  The  velocity  of  a 
tide-wave  in  a  river  seldom  exceeds  10  or  20  miles  an  hour;  and  is 
ordinarily  much  less. 


CHAPTER   VIII 

THE  PLANETARY  SYSTEM 

The  Planets  in  General  — Their  Number,  Classification,  and  Arrangement— 
Bode's  Law — Their  Orbits  —  Keplers  Lawc  and  Gravitation  —  Apparent 
Motions  and  the  Systems  of  Ptolemy  and  Copernicus — Determination  of 
Data  relating  to  the  Planets,  their  Diameter,  Mass,  etc. —  Herschel's  Illus- 
tration of  the  Solar  System — Description  of  the  Terrestrial  Planets  — 
Mercury,  Venus,  and  Mars 

216.  The  earth  is  one  of  a  number  of  bodies  called 
Planets,  i.e.,  "  wanderers,"  which  revolve  around  the  sun 
in  oval  orbits  that  are  nearly  circular  and  lie  nearly  in  one 
plane  or  level.     There  are  eight  which  are  of  considerable 
size,  besides  a  group  of  several  hundred  minute  bodies 
called  the  "asteroids,"  which  seem  to  represent  in  some 
way  a  ninth  planet,  either  broken  to  pieces,  or  somehow 
ruined  in  the  making. 

217.  Classification   of   the   Planets.  —  The    four  inner 
ones  have  been  called  by  Humboldt  the  terrestrial  planets, 
because  the  earth  is  one  of  them,  and  the  others  resemble  it 
in  size  and  density.     In  the  order  of  distance  ,from  the  sun 
they  are  Mercury,  Venus,  the  Earth,  and  Mars.    The  four 
outer  ones  Humboldt  calls  the  major  planets,  because  they 
are  much  larger  and  move  in  larger  orbits.      They  seem 
to  be  bodies  of  a  different  sort  from  the  earth,  very  much 
less  dense  and  probably  of  higher  temperature.     They  are 
Jupiter,  Saturn,  Uranus,  and  Neptune. 

188 


THE  PLANETS  IN  GENERAL 


189 


The  asteroids  (from  the  Greek  cutereido*,  i.e.,  starlike 
planets),  called  by  some  minor  planets,  lie  in  the  vacant 
space  between  Mars  and  Jupiter,  and  appear  to  contain  in 
the  aggregate  about  as  much  material  as  would  make  a 
planet  not  so  large  as  Mars. 

All  of  the  planets  except  Mercury  and  Venus  have 
satellites.  The  Earth  has  one,  Mars  two,  Jupiter  nine, 
Saturn  nine,  Uranus  four,  Neptune  one,  —  twenty-six 
in  all. 

218.  The  following  little  table  contains  in  round  num- 
bers the  principal  numerical  facts  as  to  the  planets. 


NAME 

DISTANCE  IN 
ASTRONOMICAL 
UNITS 

PERIOD 

DlAMETEll 

Mercury  

5t      0.4 

3  months 

3000  miles 

Venus 

^      07 

74-  months 

7700     " 

Earth 

^      10 

1  year 

7918     " 

if)     1.5 

1  yr   10  mos 

4200     " 

Asteroids 

3  0± 

3  years  to  9  years 

500  to  10  miles 

aO     5.2 

11.9  years 

88  000  miles 

Saturn     

*,ijk>    95 

29  5     " 

74  000     " 

Uranus    

}ioo!9.2 

84.0     " 

30,000     " 

Neptune     

3-$  <>d30.1 

164.8     " 

35  000     " 

This  table  should  be  learned  by  heart.  More  accurate 
data  will  be  given  hereafter,  but  the  round  numbers  are 
quite  sufficient  for  all  ordinary  purposes  and  are  much 
more  easily  remembered. 

219.  Bode's  Law.  —  If  we  set  down  a  row  of  4's,  to  the 
second  4  add  3,  to  the  third  6,  to  the  fourth  12,  etc.,  a 
series  of  numbers  will  result  which,  divided  by  10,  will 
represent  the  planetary  distances  very  nearly,  except  in  the 


190  LESSONS  IN  ASTRONOMY 

case  of  Neptune,  whose  distance  is  only  30  instead  of  39, 
as  the  rule  would  make  it.     Thus : 


4 
3 

7 
9 

4 

6 
10 

0 

4 
12 
16 
$ 

4 
24 

[28] 
0 

4 

48 

4 

96 

4 
192 

4 
384 

52 
It 

100 

196 

¥ 

388 

(The  characters  below  the  numbers  are  the  symbols  of  the 
planets,  used  in  almanacs  instead  of  their  names.) 

This  law  seems  to  have  been  first  noticed  by  Titius  of  Wittenberg, 
but  bears  the  name  of  Bode,  Director  of  the  Observatory  of  Berlin, 
who  first  secured  general  attention  to  it. 

No  logical  reason  can  yet  be  given  for  it.  It  may  be  a  mere  con- 
venient coincidence,  or  it  may  be  the  result  of  the  process  of  develop- 
ment, which  brought  the  solar  system  into  its  present  state. 

220.  Kepler's  Laws.  —  Three  famous  laws  discovered  by 
Kepler  (1607-1620)  govern  the  motions  of  the  planets. 

I.  The  orbit  of  each  planet  is  an  ellipse  with  the  sun  in 
one  of  its  foci.  (For  a  description  of  the  ellipse,  see  Appen- 
dix, Sec.  429.) 

II.  In  the  motion  of  each  planet  around  the  sun,  the 
radius  vector  describes  equal  areas  in  equal  times.  (For 
illustration,  see  Sec.  121,  Fig.  14.)  * 

III.  The  squares  of  the  periods  of  the  planets  are  propor- 
tional to  the  cubes  of  their  mean  distances  from  the  sun.  This 
is  known  as  the  "  Harmonic  Law."  Stated  as  a  propor- 
tion it  reads  :  Px2 :  P22 : :  A^ :  A£,  or  in  words  : 

The  square  of  the  period  of  planet  No.  1  is  to  the  square 
of  the  period  of  planet  No.  2  as  the  cube  of  the  mean  dis- 
tance of  planet  No.  1  is  to  the  cube  of  the  mean  distance  of 
planet  No.  2.  Planets  No.  1  and  No.  2  are  any  pair  of 


THE  PLANETS  IN  GENERAL         191 

planets  selected  at  pleasure.     (For  fuller  illustration,  see 
Appendix,  Sec.  430.) 

It  was  the  discovery  of  this  law  which  so  filled  Kepler 
with  enthusiasm  that  he  wrote,  "If  God  has  waited  6000 
years  for  a  discoverer,  I  can  wait  as  long  for  a  reader." 

221,  Gravitation.  —  When  Kepler  discovered  these  three 
laws  he  could  give  no  reason  for  them  —  no  more  than  we 
can  now  for  Bode's  law;  —  but  some  sixty  years  later 
Newton  showed  that  they  all  follow  necessarily  as  conse- 
quences of  the  law  of  gravitation,  which  he  had  discovered  ; 
namely,   that   "  every  particle    of  matter   in    the    universe 
attracts  every  other  particle  with  a  force  that  varies  directly 
as  the  masses  of  the  particles,  and  inversely  as  the  square  of 
the  distance  between  them"     It  would  take  us  far  beyond 
our  limits  to  attempt  to  show  how  Kepler's  laws  follow 
from  this,  but  they  do.     The  only  mystery  in  the  case  is 
the  mystery  of   the   "attraction"    itself;   for   this    word 
"  attraction "  is  to  be  taken  as  simply  describing  an  effect 
without  in  the  least  explaining  it. 

Things  take  place  as  if  the  atoms  had  in  themselves  intelligence 
to  recognize  each  other's  positions,  and  power  to  join  hands  in  some 
way,  and  pull  upon  each  other  through  the  intervening  space,  whether 
it  be  great  or  small.  But  neither  Newton  nor  any  one  else  supposes 
that  atoms  are  really  endowed  with  any  such  power,  and  the^expla- 
nation  of  gravity  remains  to  be  found.  Very  probably  it  is  somehow 
involved  in  that  constitution  of  the  material  universe  which  makes 
possible  the  transmission  of  light  and  heat  and  electric  and  mag- 
netic forces  through  space  apparently  empty,  but  probably  filled  with 
that  mysterious  substance  "  the  ether  "  of  the  physicists. 

222.  Sufficiency  of  Gravitation  to  explain  the  Planetary 
Motions.  —  We  wish  to  impress  as  distinctly  as  possible 
upon   the   student  one  idea,   this  namely,   that  given  a 


192 


LESSONS  IN  ASTRONOMY 


planet  once  in  motion,  nothing  further  than  gravitation  is 
required  to  explain  perfectly  all  its  motions  forever  after. 
Many  half-educated  people  have  an  idea  that  some  other 
force  or  mechanism  must  act  to  keep  the  planets  going. 


FIG.  49.  —  The  Smaller  Planetary  Orbits 

v  This  is  not  so :  not  a  single  motion  in  the  whole  planetary 
system  has  ever  yet  been  detected  for  which  gravitation 
fails  to -account. 

223.    Map  of  the  Orbits.  —  Fig.  49  shows   the  smaller 
orbits  of  the  system  (including  the  orbit  of  Jupiter),  drawn 


THE  PLANETS  IN  GENERAL  193 

to  scale,  the  radius  of  the  earth's  orbit  being  taken  as 
four-tenths  of  an  inch. 

On  this  scale,  the  diameter  of  Saturn's  orbit  would  be  7.4  inches, 
that  of  Uranus  would  be  13.4  inches,  and  that  of  Neptune  about 
2  feet.  The  nearest  fixed  star,  on  the  same  scale,  would  be  a  mile 
and  a  quarter  away. 

It  will  be  seen  that  the  orbits  of  Mercury,  Mars,  Jupiter, 
and  several  of  the  asteroids  are  quite  distinctly  "out  of 
center  "  with  respect  to  the  sun.  The  orbits  are  so  nearly 
circular  that  there  is  no  noticeable  difference  between  their 
length  and  their  breadth,  but  the  eccentricity  shows  plainly 
in  the  position  of  the  sun. 

224.  Inclination  of  the  Orbits.  —  The  orbits  are  drawn 
as  if  they  all  lay  on  the  plane  of  the  ecliptic,  i.e.,  on  the 
surface  of  the  paper. 
This  is  not  quite  cor- 
rect. The  orbit  of  the 
asteroid  Pallas  should 
be  really  tipped  up  at 
an  angle  of  nearly  30°, 

and  that  of   Mercury,         FIG.  50.  —  Inclination  and  Line  of  Nodes 

which  is  more  inclined 

to  the  ecliptic  than  the  orbit  of  any  other  of  the  principal 
planets,  is  sloped  at  an  angle  of  7°.  The  inclinations,  how- 
ever, are  so  small  (excepting  the  asteroids)  that  they  may  be 
neglected  for  ordinary  purposes.  On  the  scale  of  the  dia- 
gram, Neptune,  which  rises  and  falls  the  most  of  all  with  ref- 
erence to  the  plane  of  the  ecliptic,  would  never  be  more  than 
a  third  of  an  inch  above  or  below  the  level  of  the  paper. 

The  line  in  which  the  plane  of .  a  planet's  orbit  cuts  the 
plane  of  the  earth's  orbit  at  the  ecliptic  is  called  the  Line 


194 


LESSONS  IN  ASTRONOMY 


of  Nodes.     Fig.  50  shows  how  the  line  of  nodes  and,  z, 
the  inclination  of  the  two  orbits,  are  related. 

225.  Geocentric  Motions  of  the  Planets,  i.e.,  their  Motions 
with  Respect  to  the  Earth  regarded  as  the  Center  of  Obser- 
vation. — While  the  planets  revolve  regularly  in  nearly  cir- 
cular orbits  around  the  sun,  with  velocities1  which  depend 
upon  their  distance  from  it,  the  motions  relative  to  the  earth 
are  very  different,  being  made  up  of  the  planet's  real  motion 

combined  with  the  appar- 
ent motion  due  to  that 
of  the  earth  in  her  own 
orbit. 

If,  for  instance,  we 
keep  up  observations,  for 
a  long  time,  of  the  direc- 
tion of  Jupiter  as  seen 
from  the  earth,  at  the 
same  time  watching  the 
changes  of  its  distance 
by  measuring  the  alter- 
ations of  the  planet's 
apparent  size  as  seen  in 
the  telescope,  and  then  plot  the  results  to  get  the  form  of 
the  orbit  of  Jupiter  with  reference  to  the  earth,  we  get  a 
path  like  that  shown  in  Fig.  51,  which  represents  his 
motion  relative  to  the  earth  during  a  term  of  about 
twelve  years.  The  appearances  are  all  the  same  as  if  the 
earth  were  really  at  rest  while  the  planet  moved  in  this 
odd  way. 

1  Q 

1 A  planet's  velocity  in  miles  per  second  equals  very  nearly 
the  distance  being  expressed  as  in  Sec.  218. 


FIG.  51.  — Apparent  Geocentric  Motion  of 
Jupiter 


THE  PLANETS  IN  GENERAL 


195 


The  procedure  for  finding  this  relative,  or  geocentric,  orbit  of 
Jupiter  is  the  same  as  that  indicated  in  Appendix,  Sec.  428,  for  find- 
ing the  form  of  the  earth's  orbit  around  the  sun. 

226.  Direct  and  Retrograde  Motion. — With  the  eye  alone 
the  changes  in  a  planet's  diameter  would  not  be  visible, 
and  we  should  notice  only  the  alternating  direct  (eastward) 
and  retrograde  (westward)  motion  of  the  planet  among  the 
stars.  If  we  watch  one  of  the  planets  (say  Mars)  for  a 
few  weeks,  beginning  at  the  time  when  it  rises  at  sunset, 


FIG.  52.  — Apparent  Motions  of  Saturn  and  Uranus  in  1897 

we  shall  find  that  each  night  it  has  traveled  some  little 
distance  to  the  west;  and  it  will  keep  up  this  westward 
or  retrograde  motion  for  some  weeks,  when  it  will  stop  or 
become  "  stationary,"  and  will  then  reverse  its  motion 
and  begin  to  move  eastward.  If  we  watch  long  enough 
(1.0.,  for  several  years),  we  shall  find  that  it  keeps  up  this 
oscillating  motion  all  the  time,  the  length  of  its  eastward 
swing  being  always  greater  than  that  of  the  corresponding 
westward  one.  Fig.  52  shows  the  alternate  progression 
and  retrogression  of  Saturn  and  Uranus  during  1897.  All 


196 


LESSONS  IN  ASTRONOMY 


the  planets,  without  exception,  behave  alike  in  this  respect, 
as  to  their  alternate  direct  and  retrograde  motion  among 
the  stars. 

227.  Elongation  and  Conjunction.  —  The  visibility  of  a 
planet  does  not,  however,  depend  upon  its  position  among 
the  stars,  but  upon  its  position  in  the  sky  with  reference 


Conjunction 


Greatest  E. 


ion 


Opposition 
FIG.  53.  —Planetary  Configurations 

to  the  sun's  place.  If  it  is  very  near  the  sun,  it  will  be 
above  the  horizon  only  by  day,  and  generally  we  cannot 
see  it.  The  Elongation  of  a  planet  is  the  apparent  distance 
from  the  sun  in  degrees,  as  seen  from  the  earth,  of  course. 
In  Fig.  53,  for  the  planet  P,  it  is  the  angle  PES.  When 
the  planet  is  in  line  with  the  sun  as  seen  from  the  earth, 
at  B,  C,  or  I  in  the  figure,  the  elongation  is  zero,  and  the 


THE  PLANETS  IN  GENERAL  197 

planet  is  said  to  be  in  conjunction;  inferior  conjunction, 
if  the  planet  is  between  the  earth  and  the  sun,  as  at  J; 
superior,  if  beyond  the  sun,  as  at  B  or  C.  When  the 
elongation  is  180°,  as  at  A,  the  planet  is  said  to  be  in 
opposition.  When  the  planet  is  at  an  elongation  of  90°, 
as  at  F  or  G,  it  is  in  quadrature.  Evidently  only  those 
planets  which  lie  within  the  earth's  orbit,  and  are  called 
"  inferior  "  planets,  can  have  an  inferior  conjunction  ;  and 
only  those  which  are  outside  the  earth's  orbit  (the  "  supe- 
rior" planets)  can  come  to  quadrature  or  opposition. 

228.  Synodic  Period.  —  The  synodic  period  of  a  planet  is 
the  time  occupied  by  it  in  passing  from  conjunction  to  con- 
junction again,  or  from  opposition  to  opposition  ;  so  called 
because  the  word  "synod"  is  derived  from  two  Greek 
words  which  mean  "a  coming  together."  The  relation 
of  the  synodic  period  to  the  sidereal  is  the  same  for  planets 
as  in  the  case  of  the  moon.  If  E  is  the  length  of  the 
true  (sidereal)  year,  and  P  the  planet's  sidereal  period,  S 
being  the  length  of  the  synodic  period,  then 


(The  difference  between  —  and  —  is  to  be  taken  without 

Mi  JT 

regard  to  which  of  the  two  is  the  larger.) 

229.  The  Synodic  Motion,  or  Apparent  Motion  of  a  Planet 
with  Respect  to  "  Elongation  "  or  to  the  Sun's  Place  in  the 
Sky.  —  In  this  respect  there  is  a  marked  difference  between 
the  superior  and  inferior  planets. 

(a)  The  inferior  planets  are  never  seen  very  far  from 
the  sun,  but  appear  to  oscillate  back  and  forth  in  front  of 
and  behind  him.  Venus,  for  instance,  starting  at  superior 


198  LESSONS  IN  ASTRONOMY 

conjunction  at  C  (Fig.  53),  seems  to  come  out  eastward 
from  the  sun  as  an  evening  star,  until,  at  the  point  V,  she 
reaches  her  greatest  eastern  elongation,  about  47°  from  the 
sun.  Then  she  begins  to  diminish  her  elongation,  and 
approaches  the  sun,  until  she  comes  to  inferior  conjunc- 
tion, at  /.  From  there  she  continues  to  move  westward  as 
morning  star,  until  she  comes  to  V1,  her  greatest  western 
elongation,  and  there  she  begins  to  diminish  her  western 
elongation  until,  at  the  end  of  the  synodic  period,  she  is 
back  at  superior  conjunction.  The  time  taken  to  move 
from  V'  to  V  through  C  is,  in  her  case,  more  than  three 
times  that  required  to  slide  back  from  V  to  V  through  /. 

(b)  The  superior  planets  may  be  found  at  all  elonga- 
tions, and  do  not  oscillate  back  and  forth  with  reference  to 
the  apparent  place  of  the  sun,  but  continually  increase  their 
western  elongation  or  decrease  their  eastern.  They  always 
come  to  the  meridian  earlier  on  each  successive  night,  though 
the  difference  is  not  uniform.  A  superior  planet  is  known 
as  morning  star  from  the  time  it  passes  conjunction  until 
it  reaches  opposition,  when  it  rises  at  sunset ;  it  is  evening 
star  while  passing  from  opposition  back  to  conjunction. 

230.  Ptolemaic  and  Copernican  Systems.  —  Until  the 
time  of  Copernicus  (about  1540)  the  Ptolemaic  system 
prevailed  unchallenged.  It  rejected  the  idea  of  the  earth's 
rotation  (though  Ptolemy  accepted  the  rotundity  of  the 
earth),  placing  her  at  the  center  of  things  and  teaching 
that  the  apparent  motions  of  the  stars  and  planets  were 
real  ones.  It  taught  that  the  celestial  sphere  revolves  daily 
around  the  earth,  carrying  the  stars  and  planets  with  it, 
and  that  besides  this  diurnal  motion,  the  moon,  the  sun, 
and  all  the  planets  revolve  around  the  earth  within  the 


THE  PLANETS  IN  GENERAL         199 

sphere,  the  two  former  steadily,  but  the  planets  with  the 
peculiar  looped  motion  shown  in  Fig.  51. 

Copernicus  put  the  sun  at  the  center,  making  the  earth 
revolve  on  its  axis  and  travel  around  the  sun,  and  showed 
that  it  was  possible  in  this  simple  way  to  account  for  all 
the  otherwise  hopelessly  complicated  phenomena  of  the 
planetary  and  diurnal  motions,  so  far  as  then  known.  It 
was  not  until  after  the  invention  of  the  telescope  and  the 
introduction  of  new  methods  of  observation  that  the  facts 
which  absolutely  demonstrated  the  orbital  motion  of  the 
earth  were  brought  to  light,  viz.,  Aberration  of  Light 
(Appendix,  Sec.  435)  and  Stellar  Parallax  (Sec.  343). 

THE  PLANETS  THEMSELVES 

231.  In  studying  the  planetary  system  we  meet  a  num- 
ber of  inquiries  which  refer  to  the  planet  itself  and  not  to 
its  orbit,  relating,  for  instance,  to  its  magnitude  ;  its  mass, 
density,  and  surface  gravity  ;  its  diurnal  rotation  and  oblate- 
ness;  its  brightness,  phases,  and  reflecting  power,  or  "albedo"; 
the  peculiarities  of  its  spectrum  ;  its  atmosphere  ;  its  surface 
markings  and  topography  ;  and,  finally,  its  satellite  system. 

232.  Magnitude.  —  The  size  of  a  planet  is  found   by 
measuring  its  apparent  diameter  (in  seconds  of  arc)  with 
some  form  of  "micrometer."     (See  Appendix,  Sec.  415.) 
Since  we  can  find  the  distance  of  a  planet  from  the  earth 
at  any  moment  when  we  know  its  orbit,  this  micrometric 
measure  will  give  us  the  means  of  finding  at  once  the 
planet's  diameter  in  miles. 

If  we  take  r  to  represent  the  number  of  times  by  which 
the  planet's  semi-diameter  exceeds  that  of  the  earth,  then 


200  LESSONS  IN  ASTRONOMY 

the  area  of  the  planet's  surface  compared  with  that  of  the 
earth  equals  r2,  and  its  volume  or  bulk  equals  r3.  The 
nearer  the  planet,  other  things  being  equal,  the  more 
accurately  r  and  the  quantities  to  be  derived  from  it  can 
be  determined.  An  error  of  0".l  in  measuring  the  appar- 
ent diameter  of  Venus  when  nearest  us  counts  for  less 
than  thirteen  miles,  while  in  Neptune's  case,  the  same 
error  would  correspond  to  more  than  1800  miles. 

233.  Mass,  Density,  and  Gravity.  —  If  the  planet  has  a 
satellite,  its  mass  is  very  easily  and  accurately  found  from 
the  following  proportion,  which  we  simply  state  without 
demonstration  (see  General  Astronomy,  Arts.  536,  539),  viz. : 

A3     a3 

Mass  of  Sun  :  Mass  of  Planet  :  :  — -  :  — ; 

J-        t 

in  which  A  is  the  mean  distance  of  the  planet  from  the 
sun  and  T  its  sidereal  period  of  revolution,  while  a  is 
the  distance  of  the  satellite  from  the  planet  and  t  its 

sidereal  period;  whence 

/a3      T2\ 
Mass  of  Planet  =  Sun  X  I  —^  x  -p  J. 

The  calculations  indicated  are  very  easy  with  the  help  of  loga- 
rithms, and  if  the  student  has  learned  to  use  them  it  will  be  well  for 
him  to  verify  some  of  the  planet  masses  from  the  data  for  the  satel- 
lites given  in  Table  III,  p.  403. 

Substantially  the  same  proportion  may  be  used  to  compare  the 
planet  with  the  earth,  viz. : 

(Earth  +  Moon)  :  (Planet  +  Satellite)  : :  ^  :  ^; 

*i       'a 
«!  and  ^  being  here  the  period  and  distance  of  the  moon,  and  a2 

and  t2  those  of  the  planet's  satellite. 

If  the  planet  has  no  satellite,  the  determination  of  its 
mass  is  a  difficult  matter,  depending  upon  perturbations 
produced  by  it  in  the  motions  of  the  other  planets. 


THE  PLANETS  IN  GENERAL  201 

Having  the  planet's  mass  compared  with  the  earth,  we 
get  its  density  by  dividing  the  mass  by  the  volume,  and 
the  superficial  gravity  is  found  by  dividing  by  r2  the  mass 
of  the  planet  compared  with  that  of  the  earth. 

234,  The  Rotation  Period  and  Data  connected  with  it.  — 
The  length  of  the  planet's  day,  when  it  can  be  determined 
at  all,  is  ascertained  by  observing  with  the  telescope  some 
spot  on  the  planet's  disk,  and  noting  the  interval  between 
its  returns  to  the  same  apparent  position.  -The  inclination 
of  the  planet's  equator  to  the  plane  of  its  orbit,  and  the 
position   of   its   equinoxes,  are    deduced   from    the  same 
observations  that  give  the  planet's  diurnal  rotation ;   we 
have  to  observe  the  path  pursued  by  a  spot  in  its  motion 
across  the  disk.     Only  Mars,  Jupiter,  and  Saturn  permit 
us  to  find  these  elements  with  any  considerable  accuracy. 

The  ellipticity  or  oblateness  of  the  planet,  due  to  its 
rotation,  is  found  by  taking  measures  of  its  polar  and 
equatorial  diameters. 

235.  Data  relating  to  the  Planet's  Light.  —  A  planet's 
brightness  and  its  reflecting  power,  or  "  albedo,"  are  deter- 
mined by  photometric  observations,  and  the  spectrum  of  the 
planet's  light  is  of  course  studied  with  the  spectroscope. 
The  question  of  the  planet's  atmosphere  is  investigated  by 
means  of  various  effects  upon  the  planet's  appearance  and 
light,  and  by  the  phenomena  that  occur  when  the  planet 
comes  very  near  to  a  star  or  to  some  other  heavenly  body 
which  lies  beyond.      The  planet's  surface  markings  and 
topography  are  studied  directly  with  the  telescope,  by  mak- 
ing careful  drawings  of  the  appearances  noted  at  different 
times.     Photography,  also,  is  beginning  to  be  used  for 
the    purpose.     If   the  planet   has    any    well-marked  and 


LESSONS  IN  ASTRONOMY 

characteristic  spots  upon  its  surface  by  which  the  time  of 
rotation  can  be  found,  then  it  soon  becomes  easy  to  identify 
such  as  are  really  permanent,  and  after  a  time  we  can 
chart  them  more  or  less  perfectly ;  but  we  add  at  once  that 
Mars  is  the  only  planet  of  which,  so  far,  we  have  been  able 
to  make  anything  which  can  be  fairly  called  a  map. 

236.  Satellite  System.  —  The  principal  data  to  be  ascer- 
tained are  the  distances  and  periods  of  the  satellites.    These 
are  obtained  by  micrometric    measures  of    the  .apparent 
distance  and  direction  of  each  satellite  from  the  planet,  fol- 
lowed up  for  a  considerable  time.    In  a  few  cases  it  is  pos- 
sible to  make  observations  by  which  we  can  determine  the 
diameters  of  the  satellites,  and  when  there  are  a  number 
of  satellites  together  their  masses  may  sometimes  be  ascer- 
tained from  their  mutual  perturbations.    With  the  excep- 
tion of  our  moon  and  the  outer  satellites  of  Jupiter  and 
Saturn,  all  the  satellites  of  the  solar  system  move  very 
nearly  in  the  plane  of  the  equator  of  the  planet  to  which 
they  belong,  —  at  least  so  far  as  known,  for  we  do  not 
know  with  certainty  the  position  of  the  equators  of  Uranus 
and  Neptune.   Moreover,  all  the  satellites,  except  the  moon, 
Hyperion,  and  those  recently  discovered,  move  in  orbits 
that  are  very  nearly  circular. 

237.  Tables  of  Planetary  Data.  —  In  the  Appendix  we 
present  tables  of  the  different  numerical  data  of  the  solar 
system,  derived  from  the  best  authorities  and  calculated 
for  a  solar  parallax  of  8".80,  the  sun's  mean  distance  being 
therefore   taken   as    92,897000    miles.     These    tabulated 
numbers,  however,  differ  widely  in  accuracy.     The  periods 
of  the  planets  and  their  distances  in  "  astronomical  units  " 
are  very  accurately  known ;  probably  the  last  decimal  in 
the  table  may  be  trusted.     Next  in  certainty  come  the 


THE  PLANETS  IN  GENERAL 


203 


masses  of  such  planets  as  have  satellites,  expressed  in  terms 
of  the  sun's  mass.  The  masses  of  Venus  and  Mercury  are 
much  more  uncertain. 

The  distances  of  the  planets  in  miles,  their  masses  in 
terms  of  the  earth's  mass,  and  their  diameters  in  miles,  all 
involve  the  solar  parallax  and  are  affected  by  the  slight 
uncertainty  in  its  amount.  For  the  remoter  planets, 


FIG.  54.  — Kelative  Size  of  the  Planets 

diameters,  volumes,  and  densities  are  all  subject  to  a  very 
considerable  percentage  of  error.  The  student  need  not 
be  surprised,  therefore,  at  finding  serious  discrepancies 
between  the  values  given  in  these  tables  and  those  given 
in  others,  amounting  in  some  cases  to  ten  or  twenty  per 
cent,  or  even  more.  Such  differences  merely  indicate  the 
actual  uncertainty  of  our  knowledge.  Fig.  54  gives  an 
idea  of  the  relative  sizes  of  the  planets. 


204  LESSONS  IN  ASTRONOMY 

The  sun,  on  the  scale  of  the  figure,  would  be  about  a 
foot  in  diameter. 

238.  Sir  John  Herschel's  Illustration  of  the  Dimensions  of  the 
Solar  System. — In  his  "Outlines  of  Astronomy,"  Herschel  gives 
the  following  illustration  of  the  relative  magnitudes  and  distances 
of  the  members  of  our  system : 

Choose  any  well-levelled  field.  On  it  place  a  globe  two  feet  in 
diameter.  This  will  represent  the  sun.  Mercury  will  be  represented  by 
a  grain  of  mustard  seed  on  the  circumference  of  a  circle  164  feet  in 
diameter  for  its  orbit ;  Venus,  a  pea,  on  a  circle  of  284  feet  in  diameter  ; 
the  Earth,  also  a  pea,  on  a  circle  of  430  feet ;  Mars,  a  rather  large  pin's 
head,  on  a  circle  of  654  feet ;  the  asteroids,  grains  of  sand,  on  orbits  hav- 
ing a  diameter  of  1000  to  1200  feet ;  Jupiter,  a  moderate-sized  orange,  on 
a  circle  nearly  half  a  mile  across  ;  Saturn,  a  small  orange,  on  a  circle  of 
four-fifths  of  a  mile  ;  Uranus,  a  full-sized  cherry  or  small  plum,  upon  a 
circumference  of  a  circle  more  than  a  mile  in  diameter ;  and,  finally, 
Neptune,  a  good-sized  plum,  on  a  circle  about  2-J-  miles  in  diameter. 

We  may  add  that  on  this  scale  the  nearest  star  would  be  on  the 
opposite  side  of  the  earth,  8000  miles  away. 


THE   TERRESTRIAL  PLANETS  — MERCURY,  VENUS, 
AND   MARS 

MERCURY 

239.  Mercury  has  been  known  from  the  remotest  antiq- 
uity, and  among  the  Greeks  it  had  for  a  time  two  names, 
—  Apollo  when  it  was  morning  star,  and  Mercury  when  it 
was  evening  star.  It  is  so  near  the  sun  that  it  is  com- 
paratively seldom  seen  with  the  naked  eye,  but  when  near 
its  greatest  elongation  it  is  easily  enough  visible  as  a  bril- 
liant reddish  star  of  the  first  magnitude,  low  down  in  the 
twilight.  It  is  best  seen  in  the  evening  at  such  eastern 


MERCURY  205 

elongations  as  occur  in  the  spring.     When  it  is  morning 
star  it  is  best  seen  in  the  autumn. 

It  is  exceptional  in  the  solar  system  in  various  ways.  It 
is  the  nearest  planet  to  the  sun,  receives  the  most  light  and 
heat,  is  the  swiftest  in  its  movement,  and  (excepting  some 
of  the  asteroids)  has  the  most  eccentric  orbit,  with  the 
greatest  inclination  to  the  ecliptic.  It  is  also  the  smallest  in 
diameter  (again  excepting  the  asteroids),  and  has  the  least 
mass  of  all  the  planets. 

240.  Its  Orbit.  —  The  planet's  mean  distance  from  the 
sun  is  36,000000  miles,  but  the  eccentricity  of  its  orbit  is 
so  great  (0.205)  that  the  sun  is  7,500000  miles  out  of  the 
center,   and  the   distance   ranges   all  the  way  from  28 ^ 
to  43J  millions,  while  the  planet's  velocity  in  the  differ- 
ent parts  of  its  orbit  varies  from  36   miles  a  second  to 
only  23. 

A  given  area  upon  its  surface  receives  on  the  average 
nearly  seven  times  as  much  light  and  heat  as  the  same  area 
would  on  the  earth  ;  but  the  heat  received  when  the  planet 
is  at  perihelion  is  2|  times  greater  than  at  aphelion.  For 
this  reason  there  must  be  at  least  two  seasons  in  its  year, 
due  to  the  changing  distance  of  the  planet  from  the  sun, 
whatever  may  be  the  position  of  its  equator  or  the  length 
of  its  day.  The  sidereal  period  is  88  days,  and  the  syn- 
odic period  (or  time  from  conjunction  to  conjunction)  is 
116  days.  The  greatest  elongation  ranges  from  18°  to  28°, 
and  occurs  about  22  days  before  and  after  the  inferior 
conjunction.  The  inclination  of  the  orbit  to  the  ecliptic 
is  about  7°. 

241.  Planet's   Magnitude,   Mass,    etc.  —  The  apparent 
diameter  of  Mercury  varies  from  5"  to  about  13",  according 


206 


LESSONS  IN  ASTRONOMY 


to  its  distance  from  us,  and  its  real  diameter  is  very 
near  3000  miles.  This  makes  its  surface  about  ^  that  of 
the  earth,  and  its  bulk,  or  volume,  y1^.  The  planet's  mass 
is  very  difficult  to  determine,  since  it  has  no  satellite,  and 
consequently  it  is  not  accurately  known.  Probably  it  is 
about  2\  of  the  earth's  mass  ;  it  is  certainly  smaller  than 
that  of  any  other  planet  (asteroids  excepted). 

Our  uncertainty  as  to  the  mass  prevents  us  from  assign- 
ing certain  values  to  its  density  or  superficial  gravity  ;  but 
if  its  mass  as  given  above  is  correct,  it  is  probably  not 


FIG.  55.  —  Phases  of  Mercury  and  Venus 

quite  so  dense  as  the  earth,  and  the  force  of  gravity  upon 
it  is  about  one-third  what  it  is  upon  the  earth. 

242.  Telescopic  Appearances ,  Phases ,  etc .  —  Seen  through 
the  telescope  the  planet  looks  like  a  little  moon,  showing 
phases  precisely  similar  to  those  of  our  satellite.  At  infe- 
rior conjunction  the  dark  side  is  towards  us,  at  superior  con- 
junction the  illuminated  surface.  At  greatest  elongation 
the  planet  appears  as  a  half-moon.  It  is  gibbous  between 
superior  conjunction  and  greatest  elongation,  while  between 
inferior  conjunction  and  greatest  elongation  it  is  crescent. 
Fig.  55  illustrates  these  phases. 


MERCURY  20T 

The  atmosphere  of  the  planet  cannot  be  as  dense  as  that 
of  the  earth  or  Venus,  because  at  a  transit  it  shows  no 
encircling  ring  of  light,  as  Venus  does  (Sec.  248).  Both 
Huggins  and  Vogel,  however,  report  that  the  spectrum  of 
the  planet,  in  addition  to  the  ordinary  dark  lines  belonging 
to  the  spectrum  of  reflected  sunlight,  shows  certain  bands 
known  to  be  due  to  water-vapor,  thus  indicating  that  water 
exists  in  the  planet's  atmosphere. 

Generally  Mercury  is  so  near  the  sun  that  it  can  be 
observed  only  by  day,  but  when  proper  precautions  are 
taken  to  screen  the  object-glass  of  the  telescope  from  direct 
sunlight,  the  observation  is  not  especially  difficult.  The 
surface  presents  very  little  of  interest.  The  disk  is  brighter 
at  the  edge  than  at  the  center,  but  the  markings  are  not 
well  enough  denned  to  give  us  any  really  satisfactory 
information  as  to  its  topography. 

The  albedo,  or  reflecting  power,  of  the  planet  is  very 
low,  —  only  0.13,  somewhat  inferior  to  that  of  the  moon 
and  very  much  below  that  of  any  other  of  the  planets. 
No  satellite  is  known,  and  there  is  no  reason  to  suppose 
that  it  has  any. 

243.  Diurnal  Rotation  of  the  Planet.— In  1889  Schia- 
parelli,  the  Italian  astronomer,  announced  that  he  had  dis- 
covered certain  markings  upon  the  planet,  and  that  they 
showed  that  the  planet  rotates  on  its  axis  only  once  during 
its  orbital  period  of  eighty-eight  days,  thus  keeping  the 
same  face  always  turned  towards  the  sun,  in  the  same  way 
that  the  moon  behaves  with  respect  to  the  earth.  Owing 
to  the  eccentricity  of  the  planet's  orbit,  however,  it  must 
have  a  large  libration  (Sec.  145),  amounting  to  about  23£° 
on  each  side  of  the  mean  ;  i.e.,  seen  from  a  favorable  station 


208  LESSONS  IN  ASTRONOMY 

on  the  planet's  surface,  the  sun,  instead  of  rising  and  set- 
ting as  with  us,  would  seem  to  oscillate  back  and  forth 
through  an  arc  of  47°  once  in  88  days. 

This  asserted  discovery  is  very  important  and  has  excited 
great  interest.  Schiaparelli  is  probably  correct,  and  Lowell 
at  the  Flagstaff  Observatory  corroborates  him;  but  some 
are  still  skeptical,  and  it  may  be  well  to  wait  for  confir- 
mation of  his  observations  by  others  before  absolutely 
accepting  the  conclusion. 

244.  Transits  of  Mercury.  —  At  the  time  of  inferior 
conjunction  the  planet  usually  passes  north  or  south  of 
the  sun,  the  inclination  of  its  orbit  being  7°;  but  if  the 
conjunction  occurs  when  the  planet  is  very  near  its  node 
(Sec.  224),  it  crosses  the  sun's  disk  and  becomes  visible 
upon  it  as  a  small  black  spot,  —  not,  however,  large  enough 
to  be  seen  without  a  telescope,  as  Venus  can  under  similar 
circumstances.  Since  the  earth  passes  the  planet's  line  of 
nodes  on  May  7  and  November  9,  transits  can  occur  only 
near  those  days,  and  certain  peculiarities  in  the  planet's 
orbit  make  the  November  transits  about  twice  as  numerous 
as  those  that  come  in  May. 

Transits  took  place  on  May  9,  1891,  Nov.  10,  1894,  Nov.  14, 
1907,  and  Nov.  7,  1914 ;  the  next  will  occur  in  May,  1924,  and-  in 
November,  1927. 

Transits  of  Mercury  are  of  no  particular  astronomical  importance, 
except  as  furnishing  accurate  determinations  of  the  planet's  place  in 
the  sky  at  a  given  time. 


VENUS  209 


VENUS 

245.  The  second  planet  in  order  from  the  sun  is  Venus, 
the  brightest  and  most  conspicuous  of  all.    It  is  so  brilliant 
that  at  times  it  casts  a  shadow,  and  is  often  easily  seen  by 
the  naked  eye  in  the  daytime.     Like  Mercury,  it  had  two 
names  among  the  Greeks,  —  Phosphorus  as  morning  star, 
and  Hesperus  as  evening  star. 

Its  mean  distance  from  the  sun  is  67,200000  miles,  and 
its  distance  from  the  earth  ranges  from  26,000000  miles 
(93-67)tol60,000000  (93  +  67).  No  other  body  ever  comes 
so  near  the  earth  except  the  moon,  and  occasionally  a  comet. 
The  eccentricity  of  the  orbit  of  Venus  is  the  smallest  in  the 
planetary  system,  only  0.007,  so  that  the  greatest  and  least 
distances  of  the  planet  from  the  sun  differ  from  the  mean  less 
than  500,000  miles.  Its  sidereal  period  is  225  days,  or 
seven  months  and  a  half,  and  its  synodic  period  584  days, 
—  a  year  and  seven  months.  From  inferior  conjunction 
to  greatest  elongation  is  only  71  days.  The  inclination  of 
its  orbit  is  not  quite  3£°,  — less  than  half  that  of  Mercury. 

246.  Magnitude,    Mass,   Density,   etc.  —  The  apparent 
diameter  of  the  planet  varies   from  67"  at  the  time  of 
inferior  conjunction  to  only  11"  at  superior,  the  great  dif- 
ference arising  from  the  enormous  variation  in  the  distance 
of  thj  planet  from  the  earth.     The  real  diameter  of  the 
planet  in  miles  is  about  7700.     Its  surface  compared  with 
that  of  the  earth  is  T9^-;  its  volume,  -ffo.     By  means  of 
the  perturbations  she  produces  upon  the  earth,  the  mass  of 
Venus  is  found  to  be  not  quite  four-fifths  of  the  earth's 
mass,  so  that  her  mean  density  is  a  little  less  than  the 
earth's.     In  magnitude  she  is  the  earth's  twin  sister. 


210  LESSONS  IN  ASTRONOMY 

247.    General  Telescopic  Appearance,   Phases,  etc.  —  The 

general  telescopic  appearance  of  Venus  is  striking  on 
account  of  her  great  brilliancy,  but  exceedingly  unsatisfac- 
tory, because  nothing  is  distinctly  outlined  upon  the  disk. 
When  about  midway  between  greatest  elongation  and 
inferior  conjunction  the  planet  has  an  apparent  diameter 
of  40",  so  that,  with  a  magnifying  power  of  only  45,  she 
looks  exactly  like  the  moon  four  days  old,  and  of  the  same 
apparent  size.  (Very  few  persons,  however,  would  think 
so  on  the  first  view  through  the  telescope;  the  novice 
always  underrates  the  apparent  size  of  a  telescopic  object.) 

The  phases  of  Venus  were  first  discovered  by  Galileo  in  1610,  and 
afforded  important  evidence  as  to  the  truth  of  the  Copernican  system 
as  against  the  Ptolemaic. 

Fig.  56  represents  the  planet's  disk  as  seen  at  five  points  in  its  orbit. 
1,  3,  and  5  are  taken  at  superior  conjunction,  greatest  elongation,  and 
near  inferior  conjunction,  respectively,  while  2  and  4  are  at  intermedi- 
ate points.  (No.  2  is  badly  engraved,  however ;  the  sharp  corners  are 
impossible  since  a  "  terminator  "  is  always  a  semi-ellipse  (Sec.  146)). 

The  planet  attains  its  maximum  brightness  when  its 
apparent  area  is  at  a  maximum,  about  thirty-six  days  before 
and  after  inferior  conjunction.  According  to  Zollner,  the 
"  albedo  "  of  the  planet  is  0.50;  i.e.,  it  reflects  about  half  the 
light  which  falls  upon  it,  the  reflecting  power  being  about 
three  times  that  of  the  moon  and  almost  four  times  that  of 
Mercury.  It  is,  however,  slightly  exceeded  by  the  reflect- 
ing power  of  Uranus  and  Jupiter,  while  that  of  Saturn  is 
about  the  same.  The  high  albedo  is,  by  most  astronomers, 
considered  to  indicate  a  surface  mostly  covered  with  clouds, 
since  few  rocks  or  soils  could  match  its  brightness.  (But 
see  Sec.  249.)  Like  Mercury,  Mars,  and  the  moon,  the  disk 


VENUS 


211 


of  Venus  is  brightest  at  the  edge,  —  in  contrast  with  the 
appearance  of  Jupiter  and  Saturn. 

248.  Atmosphere  of  the  Planet.  —  There  is  no  question 
that  it  has  an  atmosphere  of  some  density.  When  the 
planet  is  half-way  upon  the  sun's  disk  at  the  time  of  a 
"transit,"  the  dark  part  of  the  planet  outside  the  sun  is 
encircled  by  a  thin  line  of  light  due  to  the  refraction, 


FIG.  56.  —  Telescopic  Appearances  of  Venus 

reflection,  and  scattering  of  sunlight  by  the  planet's  atmos- 
phere. And  when  the  planet  is  near  the  sun,  at  the  time 
of  inferior  conjunction,  the  horns  of  its  crescent  extend  far 
beyond  the  diameter.  When  very  near,  as  in  1898,  the 
horns  coalesce,  and  the  brightest  part  of  the  complete  ring 
is  then  on  the  side  next  the  sun,  showing  that  the  illumina- 
tion is  then  due  mainly  to  reflection  and  not  to  refraction 


212 


LESSONS  IN  ASTRONOMY 


as,. formerly  supposed.  The  height  and  density  of  its 
atmosphere  appear  to  be  about  two-thirds  as  great  as  that 
of  the  earth.  Fig.  57  represents  the  appearance  noted  by 
Vogel  during  the  transit  of  1882. 

The  presence  of  water-vapor  was  announced  by  some  of 
the  earlier  spectroscopists,  but  later  observations  fail  to 

confirm  it,  leaving 
the  fact  somewhat 
doubtful.  Many 
observers  have  also 
reported  faint  lights 
as  visible  at  times 
on  the  dark  por- 
tions of  the  planet's 
disk.  These  cannot 
be  accounted  for  by 
any  mere  reflection 
or  refraction  of  sun- 
light, but  must  orig- 
inate on  the  planet 
itself.  They  recall 
the  Aurora  Borealis 
and  other  electrical 
manifestations  on 
the  earth,  though  it  is  impossible  to  give  a  certain  expla- 
nation of  them  as  yet. 

249.  Surface  Markings,  Rotation,  etc.  —  As  has  been  said, 
Venus  is  a  very  unsatisfactory  telescopic  object.  She  pre- 
sents no  obvious  surface  markings,  — nothing  but  occasional 
indefinite  shadings.  Sometimes,  however,  when  in  the  cres- 
cent phase,  intensely  bright  spots  have  been  reported  near 


FIQ.  57.  —  Atmosphere  of  Venus  as  seen  during 
a  Transit 

Vogel,  1882 


VENUS 


213 


the  points  of  the  crescent,  which  may  perhaps  be  "  ice-caps" 
like  those  which  are  seen  on  Mars.  The  darkish  shadings 
may  possibly  be  continents  and  oceans,  dimly  visible,  but 
the  prevailing  impression  is  that  they  are  cloudlike  and 
purely  atmospheric,  the  real  surface  of  the  planet  being 
always  hidden. 

Fig.  58  is  from  drawings  made  by  Mascari  at  the  observa- 
tory on  Mt.  Etna,  and  is  an  excellent  representation  of  the 
appearance  of  the  planet  in  a  good  telescope. 


FIG.  58.  —  Venus 
After  Mascari 


As  to  the  rotation  period  of  the  planet,  nothing  is  yet 
certainly  known.  The  length  of  its  day  has  been  set,  on 
very  insufficient  grounds,  at  about  23h21m ;  but  the  recent 
work  of  Schiaparelli  makes  it  almost  certain  that  this  result 
cannot  be  trusted,  and  renders  it  rather  probable  that  Venus 
behaves  like  Mercury  in  its  diurnal  rotation,  the  length  of 
its  sidereal  day  being  equal  to  the  time  of  its  orbital  revo- 
lution. Lowell  indeed  asserts  this  positively,  but  certain 
other  observers  still  maintain  the  correctness  of  the  old 
period.  The  spectroscope  will  probably  settle  the  question 
on  Doppler's  principle  (Sec.  179),  by  showing  how  rapidly 


214  LESSONS   IN  ASTRONOMY 

the  edge  of  the  planet's  disk  moves  towards  or  from  the 
earth.  Thus  far  the  observations  rather  favor  the  longer 
period,  but  are  hardly  decisive. 

The  planet's  disk  shows  no  sensible  oblateness. 
No  satellite  has  ever  been  discovered ;  not,  however,  for 
want  of  earnest  searching. 

250.  Transits.  —  Occasionally  Venus  passes  between  the 
earth  and  the  sun  at  inferior  conjunction,  giving  us  a 
so-called  "  transit."  She  is  then  visible,  even  to  the  naked 
eye,  as  a  black  spot  on  the  sun's  disk,  crossing  it  from  east 
to  west.  When  the  transit  is  central  it  occupies  about 
eight  hours,  but  when  the  track  lies  near 
the  edge  of  the  disk  the  duration  is  cor- 
respondingly shortened.  Since  the  earth 
passes  the  nodes  of  the  orbit  on  June  5 
and  December  7,  all  the  transits  occur 
near  these  days,  but  they  are  extremely 
rare  phenomena.  Their  special  interest 

FIG.  59.  —  Transit  of    consists  in  their  availability  for  the  pur- 
Venus  Tracks  »  „    ,.        ,  ,  .,          0 

pose  of  finding  the  sun  s  parallax.    (See 

Appendix,  Sec.  437,  and  General  Astronomy,  Chap.  XVI.) 

The  first  observed  transit  in  1639  was  seen  by  only  two  persons,  — 
Horrox  and  Crabtree,  in  England, — but  the  four  which  have  occurred 
since  then  have  been  observed  in  all  parts  of  the  world  by  scientific 
expeditions  sent  out  for  the  purpose  by  the  different  governments. 
The  transits  of  1769  and  1882  were  visible  in  the  United  States. 
Transits  of  Venus  have  occurred  or  will  occur  at  the  following  dates : 

Dec.  7,  1631,       Dec.  4,  1639,       Dec.  9,  1874,       Dec.  6,  1882, 
June  5,  1761,       June  3,  1769,       June  8,  2004,       June  6,  2012. 

Fig.  58  shows  the  tracks  of  Venus  across  the  sun's  disk  during  the 
transits  of  1874  and  1882. 


MARS  215 


MARS 

251,  This  planet,  also,  has  always  been  known.  It  is  so 
conspicuous  on  account  of  its  fiery  red  color  and  brightness, 
as  well  as  the  rapidity  and  apparent  capriciousness  of  its 
movement  among  the  stars,  that  it  could  not  have  escaped 
the  notice  of  the  very  earliest  observers. 

Its  mean  distance  from  the  sun  is  a  little  more  than  one 
and  a  half  times  that  of  the  earth  (141,500000  miles),  and 
the  eccentricity  of  its  orbit  is  so  considerable  (0.093)  that 
its  radius  vector  varies  more  than  26,000000  miles.  At 
opposition  the  planet's  average  distance  from  the  earth  is 
48,600000  miles;  but  when  opposition  occurs  near  the 
planet's  perihelion  this  distance  is  reduced  to  less  than 
36,000000  miles,  while  near  aphelion  it  is  over  61,000000. 
At  conjunction  the  average  distance  from  the  earth 
is  234,000000. 

The  apparent  diameter  and  brightness  of  the  planet,  of 
course,  vary  enormously  with  these  great  changes  of  dis- 
tance. At  a  favorable  opposition  (when  the  planet's 
distance  from  us  is  the  least  possible)  it  is  more  than  fifty 
times  as  bright  as  at  conjunction  and  fairly  rivals  Jupiter ; 
when  most  remote,  it  is  hardly  as  bright  as  the  Pole-star. 

The  favorable  oppositions  occur  always  in  the  latter  part  of 
August  and  at  intervals  of  fifteen  or  seventeen  years.  The  last  such 
opposition  was  in  1909. 

The  inclination  of  the  orbit  is  small,  —  1°  51'.  The 
planet's  sidereal  period  is  687  days  (one  year,  ten  and  a 
half  months) ;  its  synodic  period  is  much  the  longest  in 
the  planetary  system,  being  780  days,  or  nearly  two  years 


216 


LESSONS  IN  ASTRONOMY 


and  two  months.     During  710  of  these  780  days  it  moves 
towards  the  east,  and  retrogrades  during  70. 

252.  Magnitude,  Mass,  etc.  —  The  apparent  diameter  of 
the  planet  ranges  from  3 ".6  at  conjunction  to  25"  at  a 
favorable  opposition.  Its  real  diameter  is  approximately 
4200  miles,  with  an  error  of  perhaps  50  miles  one  way  or 
the  other.  This  makes  its  surface  about  two-sevenths,  and 
its  volume  one-seventh  of  the  earth's.  Its  mass  is  a  little 

less  than  one-ninth  of  the 
earth's  mass,  its  density 
0.73,  and  its  superficial  grav- 
ity 0.38  ;  i.e.,  a  body  which 
here  weighs  100  pounds 
would  have  a  weight  of  only 
38  pounds  on  the  surface 
of  Mars. 

253.  General  Telescopic 
Aspect,  Phases,  etc. — When 
the  planet  is  nearest  it  is 
more  favorably  situated  for 
telescopic  observation  than 
any  other  heavenly  body, 
the  moon  alone  excepted. 
It  then  shows  a  ruddy  disk  which,  with  a  magnifying 
power  of  75,  is  as  large  as  the  moon.  Since  its  orbit 
is  outside  the  earth's,  it  never  exhibits  the  crescent 
phases  like  Mercury  and  Venus ;  but  at  quadrature  it 
appears  distinctly  gibbous,  as  in  Fig.  60,  about  like  the 
moon  three  days  from  full.  Like  Mercury,  Venus,  and  the 
moon,  its  disk  is  brightest  at  the  limb  (i.e.,  at  its  circular 
edge) ;  but  at  the  "  terminator,"  or  boundary  between  day 


FIG.  60.  —  Mars  near  Quadrature 
Lowell,  1894 


MARS  217 

and  night  upon  the  planet's  surface,  there  is  a  slight 
shading  which,  taken  in  connection  with  certain  other 
phenomena,  indicates  the  presence  of  an  atmosphere. 
This  atmosphere,  however,  is  probably  much  less  dense 
than  that  at  the  earth,  as  indicated  by  the  infrequency  of 
clouds  and  of  other  atmospheric  phenomena  familiar  to  us 
on  the  earth.  Huggins  and  Vogel  have  reported  that  the 
planet's  spectrum  shows  the  lines  of  water-vapor ;  but  the 
later  observations  of  Campbell,  at  the  Lick  Observatory, 
do  not  confirm  this  and  go  to  show  that  whatever  atmos- 
phere exists  must  be  very  rare  indeed,  not  more  than 
one-fourth  as  dense  as  our  own,  and  probably  less. 

Zollner  gives  the  albedo  of  Mars  as  0.26,  —  just  double 
that  of  Mercury,  and  much  higher  than  that  of  the  moon, 
but  only  about  half  that  of  Venus  and  the  major  planets. 
Near  opposition  the  brightness  of  the  planet  suddenly 
increases  in  the  same  way  as  that  of  the  moon  near  the 
full  (Sec.  149). 

254.  Rotation,  etc.  —  The  spots  upon  the  planet's  disk 
enable  us  to  determine  its  period  of  rotation  with  great 
precision.  Its  sidereal  day  is  found  to  be  24h37m228.67, 
with  a  probable  error  not  to  exceed  one-fiftieth  of  a  second. 
It  is  the  only  one  of  the  planets  which  has  the  length  of  its 
day  determined  with  any  such  accuracy.  The  exactness  is 
obtained  by  comparing  the  drawings  of  the  planet  made 
two  hundred  years  ago  with  others  made  recently. 

The  inclination  of  the  planet's  equator  to  the  plane  of 
its  orbit  is  very  nearly  24°  50'  (26°  21'  to  the  ecliptic}.  So 
far,  therefore,  as  depends  upon  that  circumstance,  Mars 
should  have  seasons  substantially  the  same  as  our  own,  and 
certain  phenomena  make  it  evident  that  such  is  the  case. 


218  LESSONS  IN  ASTRONOMY 

The  planet's  rotation  causes  a  slight  flattening  of  the 
poles,  —  hardly  sensible  to  observation,  but  probably  about 
2^.  (Larger  values,  now  known  to  be  erroneous,  are  given 
in  many  text-books.) 

255.  Surface  and  Topography.  —  With  even  a  small  tele- 
scope, not  more  than  four  or  five  inches  in  diameter,  the 
planet  is  a  very  beautiful  object,  showing  a  surface  diver- 
sified with  markings  light  and  dark,  which,  for  the  most 
part,  are  found  to  be  permanent.  Occasionally,  however, 
we  see  others  of  a  temporary  character,  supposed  to  be 
clouds ;  but  these  are  surprisingly  rare  as  compared  with 
clouds  upon  the  earth.  The  permanent  markings  are 
broadly  divisible  into  three  classes. 

First,  the  white  patches,  two  of  which  are  specially  con- 
spicuous near  the  planet's  poles  and  are  generally  supposed 
to  be  masses  of  snow  or  ice,  since  they  behave  just  as  would 
be  expected  if  such  were  the  case.  The  northern  one 
dwindles  away  during  the  northern  summer,  when  the  north 
pole  is  turned  towards  the  sun,  while  the  southern  one  grows 
rapidly  larger ;  and  vice  versa  during  the  southern  summer. 

Second,  patches  of  bluish  gray  or  greenish  shade,  covering 
about  three-eighths  of  the  planet's  surface  and  generally 
supposed  to  be  bodies  of  water,  though  this  is  very  far 
from  certain. 

Third,  extensive  regions  of  various  shades  of  orange  and 
yellow,  covering  nearly  five-eighths  of  the  surface,  and 
interpreted  as  land. 

These  markings  are,  of  course,  best  seen  when  near 
the  center  of  the  planet's  disk;  near  the  limb  they  are 
lost  in  the  brilliant  light  which  there  prevails,  and  at  the 
terminator  they  fade  out  in  the  shade. 


MARS 


219 


Fig.  61,  from  drawings  by  the  late  Maxwell  Green  of  Madeira, 
gives  an  excellent  idea  of  the  usual  appearance  of  the  planet  under 
favorable  conditions. 

256.  Recent  Discoveries ;  the  Canals  and  their  Gemi- 
nation.—  In  addition  to  these  three  classes  of  markings 
the  Italian  astronomer  Schiaparelli,  in  1877  and  1879, 
announced  the  discovery  of  a  great  number  of  fine  straight 
lines,  or  "canals,"  as  he  called  them, 
crossing  the  ruddy  portions  of  the 
planet's  surface  in  various  directions, 
and  in  1881  he  announced  that  many 
of  them  become  double  at  times.  For 
several  years  some  doubt  remained, 
because  other  observers,  with  tele- 
scopes more  powerful  than  his,  were 
and  still  are  unable  to  make  out  any- 
thing of  the  sort.  More  recently,  how- 
ever, his  results  have  been  confirmed 
by  several  independent  observers.  It 
appears  that  the  power  of  the  telescope 
is  not  so  important  in  the  observation 
of  these  objects  as  steadiness  of  the 
air  and  keenness  of  the  observer's  eye. 
Nor  are  they  usually  best  seen  when 
Mars  is  nearest,  but  their  visibility  depends  upon  the  sea- 
son on  the  planet ;  and  this  is  especially  the  case  with  their 
"  gemination."  There  is,  however,  considerable  reason  to 
suspect  that  this  peculiar  doubling  is  merely  an  illusion,1 
due  to  imperfect  focusing  of  the  telescope  or  a  slight 
astigmatism  of  the  observer's  eye. 

1  See  note  on  page  224. 


FIG.  61.— Telescopic 

Views  of  Mars 

Green,  1878 


220  LESSONS  IN  ASTRONOMY 

As  to  the  real  nature  of  these  markings  and  their  behav- 
ior there  is  wide  difference  of  opinion,  and  it  is  doubtful  if 
the  true  explanation  has  yet  been  proposed.  According  to 
Mr.  Lowell,  the  polar  caps  are  really  snow  masses,  which 
melt  in  the  (Martian)  spring,  and  the  water  makes  its 
way  towards  the  equator  over  the  planet's  mountainless 
plains,  obscuring  for  several  weeks  the  well-known  mark- 
ings which  are  visible  at  other  times.  For  him  the  dark  por- 
tions of  the  planet's  surface  are  not  seas,  but  land  covered 
with  vegetation  of  some  sort,  while  the  ruddy  portions  are 
rocky  deserts,  intersected  by  the  "canals,"  which,  in  his 
view,  are  really  irrigating  water  courses ;  and  on  account  of 
their  straightness  he  is  disposed  to  accept  them  as  artificial. 
When  the  waters  reach  these  canals  vegetation  springs  up 
along  their  banks  on  either  side,  and  these  streaks  of  vegeta- 
tion are  what  we  see.  Where  the  water  courses  cross  each 
other  there  are  dark  round  "lakes,"  as  they  have  been 
called,  which  he  interprets  as  oases. 

Of  course  the  difficulties  of  the  theory  are  obvious :  for 
instance,  the  almost  absolute  levelness  of  the  planet's  sur- 
face which  it  assumes,  and  especially  the  fact  that  at  Mars 
the  solar  radiation  is  only  half  as  intense  as  upon  the  earth. 
This,  recalling  the  low  density  of  his  atmosphere,  would 
naturally  lead  to  the  supposition  that  the  temperature 
even  at  his  equator  must  be  lower  than  that  at  the  sum- 
mits of  our  highest  mountains,  and  far  below  the  freez- 
ing point  of  water.  It  was  this  consideration  that  has  led 
some  astronomers  to  suggest  that  the  polar  caps  are  not  ice- 
sheets  at  all,  but  formed  of  congealed  carbon  dioxide  (CO2), 
or  some  substance  which  remains  liquid  and  vaporous  at 
much  lower  temperatures  than  water. 


MARS  221 

But  whatever  the  explanation  may  be,  there  is  no  longer 
any  doubt  that  at  the  poles  and  elsewhere  the  planet's 
surface  really  undergoes  noticeable  changes  of  appearance 
with  the  progress  of  the  planet's  seasons,  as  shown  by 
Fig.  62,  from  drawings  made  by  Barnard  at  the  Lick 
Observatory  in  1894.  At  the  same  time  Professor  Holden 
of  the  Lick  Observatory  says  that  during  the  years  1888- 
1895  nothing  has  been  observed  there,  so  far  as  he  knows, 
which  goes  to  confirm  Mr.  Lowell's  "very  positive  and 
striking  conclusions." 

The  day  may  perhaps  come  when  photography  will 
lend  further  aid  to  the  solution  of  the  problem,  or  some 


FIG.  62.  —  Seasonal  Changes  on  Mara 
Barnard 

heat  measurer  may  be  contrived  sensitive  enough  to  give 
us  positive  information  as  to  the  planet's  temperature.  If 
the  polar  caps  are  really  caps  of  frozen  water,  Mars  must 
obtain  surface  heat  from  some  still  unexplained  supply. 

257.  Maps  of  the  Planet.  —  A  number  of  maps  of  Mars  have 
been  constructed  by  different  observers  since  the  first  one  was  made 
by  Maedler  in  1830.  Fig.  63  is  reduced  from  one  which  was  pub- 
lished in  1888  by  Schiaparelli  and  shows  most  of  his  "canals"  and 
their  "geminations."  While  there  may  be  some  doubt  as  to  the 
reality  of  the  canal  system,  there  can  be  no  doubt  that  the  main 
features  of  the  planet's  surface  are  substantially  correct.  The  nomen- 
clature, however,  is  in  a  very  unsettled  state.  Schiaparelli  has  taken 


222  LESSONS  IN  ASTRONOMY 

his  names  mostly  from  ancient  geography,  while  the  English  areog- 
raphers,1  following  the  analogy  of  the  lunar  maps,  have  mainly  used 
the  names  of  astronomers  who  have  contributed  to  our  knowledge 
of  the  planet's  surface. 

258.  Satellites.  — The  planet  has  two  satellites,  discov- 
ered by  Professor  Hall,  at  Washington,  in  1877.  They 
are  extremely  small  and  observable  only  with  very  large 
telescopes.  The  outer  one,  Deimos,  is  at  a  distance  of 
14,600  miles  from  the  planet's  center  and  has  a  sidereal 
period  of  30h18m;  while  the  inner  one,  Phobos,  is  at  a  dis- 
tance of  only  5800  miles  and  its  period  is  only  7h39m,  — 
less  than  one-third  of  the  planet's  day.  (This  is  the  only 
case  of  a  satellite  with  a  period  shorter  than  the  day  of  its 
primary.)  Owing  to  this  circumstance,  it  rises  in  the  west, 
as  seen  from  the  planet's  surface,  and  sets  in  the  east,  com- 
pleting its  strange  backward  diurnal  revolution  in  about 
eleven  hours.  Deimos,  on  the  other  hand,  rises  in  the 
east,  but  takes  nearly  132  hours  in  its  diurnal  circuit, 
which  is  more  than  four  of  its  months.  Both  the  orbits 
are  sensibly  circular  and  lie  very  closely  in  the  plane  of 
the  planet's  equator. 

Micrometric  measures  of  the  diameters  of  such  small  objects  are 
impossible  ;  but,  from  photometric  observations,  Professor  E.  C.  Pick- 
ering, assuming  that  they  have  the  same  reflecting  power  as  that  of 
Mars  itself,  estimates  the  diameter  of  Phobos  as  about  7  miles,  and 
that  of  Deimos  as  5  or  6.  Lowell,  however,  from  his  observations 
of  1894,  deduces  considerably  larger  values,  viz.,  10  miles  for  Deimos 
and  36  for  Phobos.  If  this  is  correct,  Phobos,  when  in  the  zenith  of 
an  observer  on  the  planet's  surface,  would  be  about  as  large  as  the 
moon,  but  not  so  bright.  Deimos  would  be  about  as  bright  as  Venus. 

1  The  Greek  name  of  Mars  is  Ares;  hence  "Areography "  is  the 
description  of  the  surface  of  Mars. 


224  LESSONS  IN  ASTRONOMY 

259.  Habitability  of  Mars.  —  As  to  this  question  we  can  only 
say  that,  while  the  conditions  on  Mars  are  certainly  very  different 
from  those  prevailing  on  the  earth,  the  difference  is  less  than  in  the 
case  of  any  other  heavenly  body  which  we  can  see  with  our  present 
means  of  observation;  and  if  life,  such  as  we  know  life  upon  the 
earth,  can  exist  upon  any  of  them,  Mars  is  the  place.  It  is  much 
more  probable,  however,  that  the  conditions  as  to  temperature  and 
atmosphere  differ  from  our  own  quite  enough  to  preclude  all  terres- 
trial forms  of  life. 

There  is  at  present  no  scientific  ground  for  belief  one  way  or  the 
other  as  to  the  habitability  of  "  other  worlds  than  ours,"  passionately 
as  the  doctrine  has  been  affirmed  and  denied  by  men  of  opposite 
opinions. 

NOTE  TO  SECTION  256 

Experiments  recently  made  by  various  observers  upon  maps  and 
models  viewed  from  different  distances  by  sketchers  ignorant  as  to  what 
they  ought  to  see  and  draw,  strongly  confirm  the  suspicion  that  illusions 
probably  enter  to  some  extent  into  the  now  generally  accepted  repre- 
sentations of  the  surface  of  Mars,  —  illusions  due  to  a  perfectly 
honest  misinterpretation  of  actual  markings  seen  imperfectly.  The 
experiments  show  in  many  persons  a  strong  tendency  to  see  as  defi- 
nite lines  what  are  really  only  the  boundaries  of  faint  shadings,  or 
more  or  less  irregular  rows  of  separate  spots.  The  so-called  "canals" 
doubtless  represent  really  existing  features,  but  are  probably  less 
definite  and  regular  than  shown  on  our  maps. 

In  1904-1905  Mr.  Lampland,  the  photographer  of  the  Flagstaff 
Observatory,  obtained  photographs  of  Mars  far  superior  to  any  pre- 
viously made.  They  are  about  a  quarter  of  an  inch  in  diameter  and 
under  a  magnifier  show  nearly  all  the  features  of  the  planet  visible 
in  ordinary  telescopes.  Mr.  Lowell  considers  that  they  fully  confirm 
his  own  peculiar  observations.  An  expedition  sent  by  him  in  1907 
to  northern  Chile,  in  charge  of  Professor  Todd,  is  reported  to  have 
obtained  photographs  of  the  planet  showing  many  of  the  canals,  and 
some  of  them  double.  Similar  photographs  were  also  obtained  in 
1909. 


CHAPTER   IX 

THE  PLANETS  (Continued) 

The  Asteroids  —  Intramercurian  Planets  and  the  Zodiacal  Light  —The  Major 
Planets,  Jupiter,  Saturn,  Uranus,  and  Neptune 

THE  ASTEROIDS  OR  MINOR  PLANETS 

260,  The  asteroids1  are  a  multitude  of  small  planets 
circling  around  the  sun  in  the  space  between  Mars  and 
Jupiter.  It  was  early  noticed  that  between  Mars  and 
Jupiter  there  is  a  gap  in  the  series  of  planetary  distances, 
and  when  Bode's  law  (Sec.  219)  was  published  in  1772 
the  impression  became  very  strong  that  there  must  be 
a  missing  planet  in  the  space,  —  an  impression  greatly 
strengthened  when  Uranus  was  discovered  in  1781,  at  a 
distance  precisely  corresponding  to  that  law. 

The  first  member  of  the  group  was  found  by  the  Sicilian 
astronomer,  Piazzi,  on  the  very  first  night  of  the  nine- 
teenth century  (Jan.  1,  1801).  He  named  it  Ceres,  after 
the  tutelary  divinity  of  Sicily.  The  next  year  Pallas  was 
discovered  by  Olbers.  Juno  was  found  in  1 804  by  Harding, 
and  in  1807  Olbers,  who  had  broached  the  theory  of  an 
exploded  planet,  discovered  the  fourth,  Vesta,  the  only 
one  which  is  ever  bright  enough  to  be  easily  seen  by  the 

1  They  were  first  called  asteroids  (i.e.,  "starlike"  bodies)  by  Sir 
William  Herschel  early  in  the  century,  because,  though  really  planets, 
the  telescope  shows  them  only  as  stars,  without  a  sensible  disk. 

225 


226  LESSONS  IN  ASTRONOMY 

naked  eye.  The  search  was  kept  up  for  some  years  longer, 
but  without  success,  because  the  searchers  did  not  look  for 
small  enough  objects.  The  fifth  asteroid  (Astrsea)  was 
found  in  1845  by  Hencke,  an  amateur,  who  had  resumed 
the  subject  by  studying  the  fainter  stars.  In  1847  three 
more  were  discovered,  and  every  year  since  then  has  added 
from  one  to  a  hundred.  They  are  usually  designated  by 
their  "  numbers,"  but  all  the  older  ones  also  have  names : 
thus,  Ceres  is  <D,  Thule  is  (279),  Eros  is  (433),  etc.  At  pres- 
ent more  than  eight  hundred  are  known,  and  since 
1891  the  catalogue  has  been  growing  with  rather  incon- 
venient rapidity  on  account  of  the  substitution  of  pho- 
tography for  the  old-fashioned  method  of  planet-hunting. 
A  large  camera  is  strapped  on  the  back  of  a  telescope 
driven  by  clockwork,  and  a  negative,  covering  from  5°  to 
10°  square  of  the  heavens,  is  taken  with  an  exposure  of 
several  hours.  The  thousands  of  stars  that  appear  upon 
the  plate  all  show  neat  round  disks,  if  the  observer  has 
kept  his  telescope  steadily  pointed;  but  if  there  is  a 
planet  anywhere  in  the  field  it  will  move  quite  percep- 
tibly during  the  long  exposure,  and  its  image  upon  the 
plate  will  be,  not  a  dot,  but  a  streak,  which  can  be 
recognized  at  a  glance.  Sometimes  as  many  as  seven 
planets  thus  "show  up"  upon  a  single  plate,  —  old  ones 
as  well  as  new  of  course;  but  a  few  nights'  observation 
will  usually  furnish  data  from  which  the  orbits  can  be 
computed  with  sufficient  accuracy  to  decide  all  doubtful 
questions.  Max  Wolf  of  Heidelberg,  who  first  introduced 
the  method,  and  Charlois  of  Nice  have  been  especially 
successful  in  this  kind  of  asteroid-hunting.  Rev.  J.  H. 
Metcalf  of  Taunton,  Mass.,  has  recently  introduced  an 


THE  ASTEROIDS  227 

effective  modification  of  this  method,  letting  the  stars  trail, 
while  asteroid  images  are  nearly  round. 

261.  Their  Orbits.  —  The  mean  distances  of  the  different 
asteroids  from  the  sun  differ  pretty  widely,  and  the  periods, 
of  course,  correspond.     Eros,  (433),  has  by  far  the  smallest 
orbit,  its  mean  distance  from  the  sun  being    only  1.46 
(135,500000  miles),  and  its  period  643,  even  less  than  that 
of  Mars.    The  next  in  proximity  to  the  sun  is  Hungaria,  (434), 
with  a  mean  distance  of  180,000000  miles,  and  a  period  of 
three  years  and  three  days.    The  most  remote  are  Achilles, 
Patroclus,  and  Hector,  whose  orbits  do  not  differ  greatly 
from  that  of  Jupiter  in  size  and  period. 

The  inclinations  of  the  orbits  to  the  ecliptic  average 
nearly  8°.  The  orbit  of  Pallas,  ©,  is  inclined  at  an  angle 
of  35°,  and  several  others  exceed  25°.  The  eccentricity  of 
the  orbits  is  very  large  in  many  cases.  Albert,  one  of  the 
minor  planets  discovered  in  1911,  has  the  largest  eccen- 
tricity (0.54),  and  several  others  have  an  eccentricity  ex- 
ceeding 0.30.1  It  should  be  noted  that  the  orbits  of  these 
planets  are  subject  to  very  great  disturbances  from  the 
attraction  of  Jupiter,  and  this  makes  the  calculation  of 
their  motions  much  more  laborious  than  that  of  the  larger 
planets.  Very  few  of  them,  therefore,  are  followed  up 
closely ;  only  those  that  for  some  reason  or  other  possess 
a  special  interest  at  some  given  time. 

262.  The  Bodies  themselves.  —  The  four  first  discovered, 
and  one  or  two  others,  when  examined  with  a  powerful 
telescope,  show  disks  that  are  perceptible,  but  too  small 
for   satisfactory   measurement   with   ordinary   telescopes. 
By  photometric  observations,  assuming  —  what  is  by  no 

i  Ocllo  has  an  eccentricity  of  0.38. 


228  LESSONS  IN  ASTRONOMY 

means  certain  —  that  their  albedo  is  about  the  same  as  that 
of  Mars,  it  has  been  estimated  that  Vesta,  the  brightest, 
has  a  diameter  of  about  320  miles,  and  that  the  other  three 
of  the  first  four  may  be  two-thirds  as  large.  In  1895, 
however,  Mr.  Barnard  of  the  Lick  Observatory  measurecl 
the  diameters  of  Ceres,  Pallas,  and  Vesta,  micrometrically, 
and  obtained  results  that  differ  from  these  very  widely, 
and  should  probably  be  preferred.  He  finds  Ceres  to  be 
the  largest,  with  a  diameter  of  488  miles.  For  Pallas, 
Vesta,  and  Juno  he  gets  diameters  of  304,  248,  and 
118  miles,  respectively.  None  of  the  rest  can  well  exceed 
100  miles;  and  the  more  newly  discovered  ones,  which 
are  just  fairly  visible  in  a  telescope  with  an  aperture  of 
10  or  12  inches,  cannot  be  many  times  larger  than  the 
moons  of  Mars,  — say  from  10  to  20  miles  in  diameter. 

As  to  the  individual  masses  and  densities,  we  have  no 
certain  knowledge. 

Assuming  the  correctness  of  Barnard's  measures,  and  that  the 
density  of  Ceres  is  about  the  same  as  that  of  the  rocks  which  com- 
pose the  earth's  crust,  her  mass  may  be  as  great  as  ^y1^  that  of  the 
earth.  If  so,  gravity  on  her  surface  would  be  about  -fa  of  gravity 
here,  so  that  a  body  would  fall  about  seven  inches  in  the  first  second. 
Of  course,  on  the  smaller  asteroids  it  would  be  much  less. 

From  the  perturbations  of  Mars,  Leverrier  has  estimated 
that  the  aggregate  mass  of  the  whole  swarm  cannot  exceed 
one-fourth  the  mass  of  the  earth,  —  something  more  than 
double  that  of  Mars ;  a  more  recent  calculation  by  Ravene 
puts  the  limit  as  low  as  one  per  cent. 

The  united  mass  of  those  at  present  known  would  make  only  a 
small  fraction  of  such  a  body,  —  hardly  a  thousandth  of  it ;  probably, 
however,  those  still  undiscovered  are  very  numerous. 


THE   ASTEROIDS  229 

262*.  Eros.  —  The  most  interesting  of  these  little  bodies 
from  the  astronomical  point  of  view  is  Eros,  (433),  dis- 
covered by  Witt  at  Berlin  in  1898. 

Its  mean  distance  and  period,  as  already  stated,  are  less 
than  those  of  Mars,  but  the  eccentricity  of  its  orbit  (0.22) 
is  such  that  it  goes  far  outside  the  Martial  orbit  at  aphe- 
lion, while  at  perihelion  it  comes  within  13,500000  miles 
of  the  orbit  of  the  earth.  This  is  only  a  little  more  than 
half  the  nearest  approach  of  Venus,  and  gives  the  planet 
immense  importance  as  a  means  of  determining  the  solar 
parallax  by  the  method  explained  in  Sec.  468  of  the 
Manual.  But  it  is  only  when  the  perihelion  passage 
occurs  about  January  20  that  the  earth  is  rightly  situated 
to  utilize  the  conditions,  and  unfortunately  these  close 
approaches  are  very  rare. 

One  occurred  in  1894,  before  the  discovery  of  the 
planet;  the  next  will  be  in  1931.  But  in  the  winter  of 
1900—1901  the  conditions  were  better  than  they  will  be 
again  for  thirty  years,  the  nearest  approach  being  within 
about  30,000000  miles.  An  enormous  number  of  obser- 
vations were  made,  both  visual  and  photographic,  the 
results  of  which  will  require  some  years  for  their  complete 
discussion. 

The  planet's  inclination  is  about  11°,  so  that  at  the 
time  of  a  close  opposition  it  moves  among  the  stars  nearly 
from  north  to  south,  instead  of  retrograding  from  east  to 
west  like  other  planets. 

It  is  very  small,  probably  less  than  twenty  miles  in 
diameter,  and  seldom  visible  except  in  great  telescopes ;  at 
its  close  approaches,  however,  it  may  become  nearly  bright 
enough  to  be  visible  by  the  naked  eye. 


230  LESSORS  IK  ASTRONOMY 

In  certain  positions  relative  to  the  earth  there  is  a 
marked  periodic  variation  of  its  light,  and  from  this 
Director  Pickering  of  Harvard  has  deduced  by  photomet- 
ric observations  a  rotation  period  of  about  5i  hours.  One 
or  two  other  asteroids  are  suspected  of  similar  behavior, 
and  are  also  under  observation. 

263.  Origin.  —  As  to  this  we  can  only  speculate.     It  is 
hardly  possible  to  doubt,  however,  that  this  swarm  of  little 
rocks  in  some  way  represents  a  single  planet  of  the  "  ter- 
restrial "  group.     A  commonly  accepted  view  is  that  the 
material,  which,  according  to  the  nebular  hypothesis,  once 
formed  a  ring  (like  one  of  the  rings  of  Saturn),  and  ought 
to  have  collected  to  make  a  single  planet,  has  failed  to 
be  so  united ;  and  the  failure  is  ascribed  to  the  perturba- 
tions produced  by  the  next  neighbor,  the  giant  Jupiter, 
whose  powerful  attraction  is  supposed  to  have  torn  the 
ring  to  pieces,  and  thus  prevented  its  normal  development 
into  a  planet. 

Another  view  is  that  the  asteroids  may  be  fragments  of 
an  exploded  planet.  If  so,  there  must  have  been  not  one 
but  many  explosions,  —  first  of  the  original  body,  and  then 
of  the  separate  pieces ;  for  it  is  demonstrable  that  no  single 
explosion  could  account  for  the  present  tangle  of  orbits. 

INTRAMERCURIAN   PLANETS   AND  THE   ZODIACAL 
LIGHT 

264.  Intramercurian  Planets.  —  It  is  very  possible,  indeed  not 
improbable,  that  there  is  a  considerable  quantity  of  matter  circu- 
lating around  the  sun  inside  the  orbit  of  Mercury.     It  has  been 
somewhat  persistently  supposed  that  this  intramercurian  matter  is 
concentrated  into  one,  or  possibly  two,  planets  of  considerable  size, 


THE  ZODIACAL  LIGHT  231 

and  such  a  planet  has  several  times  been  reported  as  discovered,  and 
has  even  been  named  Vulcan.  The  supposed  discoveries  have  never 
been  confirmed,  however,  and  the  careful  observations  of  total  solar 
eclipses  during  the  past  ten  years  make  it  practically  certain  that 
there  is  no  "  Vulcan."  Possibly,  however,  there  is  a  family  of  intra- 
mercurian  asteroids ;  but  they  must  be  very  minute  or  some  of  them 
would  certainly  have  been  found  either  during  eclipses  or  crossing 
the  sun's  disk;  a  planet  as  much  as  200  miles  in  diameter  could 
hardly  have  escaped  discovery.  Recently  attempts  have  been  made 
to  detect  any  existing  body  of  this  kind  by  photographing  the  region 
of  the  sky  in  the  neighborhood  of  the  sun  during  a  total  solar  eclipse. 
None  has  yet  been  found. 

265.  The  Zodiacal  Light.  —  This  is  a  faint,  ill-defined 
pyramidal  beam  of  light  extending  from  the  sun  both  ways 
along  the  ecliptic.  In  the  evening  it  is  best  seen  in  the 
early  spring,  and  in  our  latitude  then  extends  about  90° 
eastward  from  the  sun ;  in  the  tropics  it  is  said  that  it  can 
be  followed  quite  across  the  sky.  The  region  near  the  sun 
is  fairly  bright  and  even  conspicuous,  but  the  more  distant 
portions  are  extremely  faint  and  can  be  observed  only  in 
places  where  there  is  no  illumination  of  the  air  by  artificial 
lights.  At  the  point  opposite  the  sun  in  the  heavens  there 
is  also  a  faint  patch  of  light,  ten  degrees  or  so  in  diameter, 
known  as  the  G-egenschein,  or  "  counter  glow." 

The  spectrum  of  the  zodiacal  light  is  a  simple,  con- 
tinuous spectrum  without  markings  of  any  kind,  so  far 
as  can  be  observed.  We  emphasize  this  because  of  late  it 
is  often  mistakenly  stated  that  the  bright  line  which  char- 
acterizes the  spectrum  of  the  Aurora  Borealis  appears  in 
the  spectrum  of  the  zodiacal  light. 

The  cause  of  the  phenomenon  is  not  certainly  known. 
Some  imagine  that  the  zodiacal  light  is  only  an  extension 


232  LESSONS  IN  ASTRONOMY 

of  the  solar  corona  (whatever  that  may  be),  which  is  not 
perhaps  unlikely;  but  on  the  whole  the  more  prevalent 
opinion  seems  to  be  that  it  is  due  to  sunlight  reflected  from 
myriads  of  small  meteoric  bodies  circling  around  the  sun, 
nearly  in  the  plane  of  the  ecliptic,  thus  forming  a  thin  flat 
sheet  (something  like  one  of  Saturn's  rings),  which  extends 
far  beyond  the  orbit  of  the  earth.  As  to  the  Gegenschein, 
it  is  generally  ascribed  to  a  brightening  up  of  the  little 
bodies  when  they  come  opposite  to  the  sun,  similar  to  the 
moon's  great  increase  of  brightness  at  the  full  (Sec.  149). 

THE  MAJOR   PLANETS  — JUPITER,   URANUS,   AND 
NEPTUNE 

JUPITER 

266.  Jupiter,  the  nearest  of  the  major  planets,  stands 
next  to  Venus  in  the  order  of  brilliance  among  the  heavenly 
bodies,  being  fully  five  or  six  times  as  bright  as  Sirius,  and 
decidedly  superior  to  Mars,  even  when  Mars  is  nearest.  It 
is  not,  like  Venus,  confined  to  the  twilight  sky,  but  at  the 
time  of  opposition  dominates  the  heavens  all  night  long. 

Its  orbit  presents  no  marked  peculiarities.  The  mean 
distance  of  the  planet  from  the  sun  is  a  little  more  than 
five  astronomical  units  (483,000000  miles),  and  the  eccen- 
tricity of  the  orbit  is  not  quite  ^,  so  that  the  actual  dis- 
tance ranges  about  21,000000  miles  each  side  of  the  mean. 
At  an  average  opposition  the  planet's  distance  from  the 
earth  is  about  390,000000  miles,  while  at  conjunction  it  is 
distant  about  580,000000. 

The  inclination  of  its  orbit  to  the  ecliptic  is  only  1°  19'. 
Its  sidereal  period  is  11.86  years,  and  the  synodic  is  399 


JUPITER  233 

days  (a  figure  easily  remembered),  a  little  more  than  a  year 
and  a  month ;  i.e.,  each  year  Jupiter  comes  to  opposition  a 
month  and  four  days  later  than  in  the  preceding  year. 

267.  Dimensions,   Mass,   Density,   etc.  —  The  planet's 
apparent  diameter  varies  from  50"  to  32",  according  to  its 
distance  from  the  earth.     The  disk,  however,  is  distinctly 
oval,  so  that  while  the  equatorial  diameter  is  nearly  90,000 
miles,  the  polar  diameter  is  only  84,200.    The  mean  diameter 
(see  Sec.  112)  is  88,000  miles,  a  little  more  than  eleven 
times  that  of  the  earth. 

These  values  are  from  recent  measures  by  Barnard  and  See,  and 
quite  possibly  need  correction  for  irradiation.  They  are  notably 
larger  than  those  determined  by  earlier  observers  with  a  different 
kind  of  micrometer  and  given  in  Table  II  of  the  Appendix.  Very 
likely  the  truth  is  intermediate. 

Its  surface,  therefore,  is  122,  and  its  volume  or  bulk  1355, 
times  that  of  the  earth.  It  is  by  far  the  largest  of  all  the 
planets,  —  larger,  in  fact,  than  all  the  rest  united. 

Its  mass  is  very  accurately  known,  both  by  means  of 
its  satellites  and  from  the  perturbations  it  produces  upon 
certain  asteroids.  It  is  y-Q\^  of  the  sun's  mass,  or  about 
316  times  that  of  the  earth. 

Comparing  this  with  its  volume,  we  find  its  mean  density 
to  be  0.24,  i.e.,  less  than  one-fourth  the  density  of  the 
earth  and  almost  precisely  the  same  as  that  of  the  sun. 
Its  surface  gravity  is  about  two  and  two-thirds  times  that 
of  the  earth,  but  varies  nearly  twenty  per  cent  between  the 
equator  and  poles  of  the  planet  on  account  of  the  rapid 
rotation. 

268.  General  Telescopic  Aspect,  Albedo,  etc.  —  In  a  small 
telescope  the  planet  is  a  fine   object;  for  a  magnifying 


234  LESSONS  IN  ASTRONOMY 

power  of  only  60  makes  its  apparent  diameter,  even  when 
remotest,  equal  to  that  of  the  moon.  With  a  large  instru- 
ment and  a  magnifying  power  of  200  or  300  it  is  magnifi- 
cent, the  disk  being  covered  with  an  infinite  variety  of 
detail,  interesting  in  outline  and  rich  in  color,  changing 
continually  as  the  planet  turns  on  its  axis.  For  the  most 
part,  the  markings  are  arranged  in  "  belts  "  parallel  to  the 
planet's  equator,  as  shown  in  Fig.  64. 

This  is  from  an  admirable  drawing  made  in  1889  by  the  late 
lamented  Keeler,  and  still  continues  to  be  an  excellent  represen- 
tation of  the  planet,  wanting  only  the  varied  colors  to  make  it 
perfect. 

Near  the  limb  the  light  is  less  brilliant  than  in  the  center 
of  the  disk,  and  the  belts  there  fade  out.  The  planet  shows 
no  perceptible  phases,  but  the  edge  which  is  turned  away 
from  the  sun  is  usually  sensibly  darker  than  the  other. 
According  to  Zdllner,  the  mean  albedo  of  the  planet  is  0.62, 
which  is  extremely  high,  that  of  white  paper  being  only 
0.78.  The  question  has  been  raised  whether  Jupiter  is 
not  to  some  extent  self-luminous,  but  there  is  no  proof,  and 
little  probability,  that  such  is  the  case. 

269.  Atmosphere  and  Spectrum.  —  The  planet's  atmos- 
phere must  be  very  extensive.  The  forms  which  we  see 
with  the  telescope  are  all  evidently  atmospheric.  In  fact, 
the  low  mean  density  of  the  planet  makes  it  very  doubtful 
whether  there  is  anything  solid  about  it  anywhere,  — 
whether  it  is  anything  more  than  a  ball  of  fluid,  overlaid 
by  cloud  and  vapor. 

The  spectrum  of  the  planet  differs  less  from  that  of  mere 
reflected  sunlight  than  might  have  been  expected,  showing 
that  the  light  is  not  obliged  to  penetrate  the  atmosphere 


1889,JULYlOd8h45nPST. 


FIG.  64.  —  Jupiter 

After  drawings  by  Keeler,  at  Lick  Observatory 
235 


236  LESSONS  IN  ASTRONOMY 

to  any  great  depth  before  it  encounters  the  reflecting 
envelope  of  cloud.  There  are,  however,  certain  unex- 
plained dark  shadings  in  the  red  and  orange  parts  of  the 
spectrum  that  are  probably  due  to  the  planet's  atmosphere, 
and  seem  to  be  identical  in  position  with  certain  bands 
which,  in  the  spectra  of  Uranus  and  Neptune,  are  much 
more  intense. 

270.  Rotation.  —  Jupiter  rotates  on  its  axis  more  swiftly 
than  any  other  of  the  planets.     Its  sidereal  day  has  a  length 
of  about  9h55m ;  but  the  time  can  be  given  only  approxi- 
mately, because  different  results  are  obtained  from  differ- 
ent spots,  according  to  their  nature  and  their  distance 
from  the  equator,  —  the  differences  amounting  to  six  or 
seven  minutes  as  determined  by  spots  of  different  char- 
acter and  in  different  latitudes.     White  spots  generally  make 
the  circuit  quicker  than  dark  spots  near  them. 

In  consequence  of  the  swift  rotation,  the  planet's  oblate- 
ness,  or  "  polar  compression,"  is  quite  noticeable, — about  -fa. 
The  inclination  of  the  planet's  equator  to  its  orbit  is  only 
3°,  so  that  there  can  be  no  well-marked  seasons  on  the 
planet  due  to  such  causes  as  produce  our  own  seasons. 

271.  Physical  Condition.  —  This  is  obviously  very  dif- 
ferent from  that  of  the  earth  or  Mars.     No  permanent 
markings  are  found  upon  the  disk,  though  occasionally 
there  are  some  which  may  be  called  "  sub-permanent,"  as, 
for  instance,  the  great  red  spot,  shown  in  Fig.  64.     This 
was  first  noticed  in  1878,  became  extremely  conspicuous 
for  several    years,    and   is    still   visible,    though    only   a 
faded  ghost  of  itself.     Were  it  not  that  during  the  first 
eight  years  of  its  visibility  it  changed  the  length  of  its 
apparent  rotation  by  about  six  seconds  (from  9h55m348.9  to 


JUPITER  237 

9h55m408.2),  we  might  suppose  it  permanently  attached 
to  the  planet's  surface,  and  evidence  of  a  coherent  mass 
underneath.  As  it  is,  opinion  is  divided  on  this  point; 
the  phenomenon  is  as  puzzling  as  the  canals  of  Mars. 

Many  things  in  the  planet's  appearance  indicate  a  high 
temperature,  as,  for  instance,  the  abundance  of  clouds  and 
the  swiftness  of  their  transformations ;  and  since  on  Jupi- 
ter the  solar  light  and  heat  are  only  Jy  as  intense  as  here, 
we  are  forced  to  conclude  that  it  gets  very  little  of  its 
heat  from  the  sun,  but  is  probably  hot  on  its  own  account, 
and  for  the  same  reason  that  the  sun  is  hot,  viz.,  as  the 
result  of  a  process  of  condensation.  In  short,  it  appears 
very  probable  that  the  planet  is  a  sort  of  semi-sun,  —  hot, 
though  not  so  hot  as  to  be  sensibly  self-luminous. 

272.  Satellites.  —  Jupiter  has  nine  satellites,  four  of 
them  large  and  easily  seen  with  a  very  small  telescope.  The 
fifth,  found  by  Barnard  in  1892,  and  the  sixth  and  seventh 
by  Perrine,  on  photographs,  in  1905  (all  at  Mt.  Hamilton), 
are  extremely  small,  and  visible  only  in  great  telescopes. 

The  four  large  satellites  were  the  first  heavenly  bodies 
ever  discovered.  Galileo  found  them  in  January,  1610, 
within  a  few  weeks  after  the  invention  of  his  telescope. 

These  are  now  usually  known  as  the  first,  second,  etc., 
in  the  order  of  their  distance  from  the  planet.  The  dis- 
tances range  from  262,000  to  1,169000  miles,  being 
respectively  6,  9,  15,  and  26  radii  of  the  planet  (nearly). 
Their  sidereal  periods  range  from  42  hours  to  16 f  days. 
Their  orbits  are  sensibly  circular  and  lie  very  nearly  in 
the  plane  of  the  equator.  The  third  satellite  is  much  the 
largest,  having  a  diameter  of  about  3600  miles,  while  the 
others  are  between  2000  and  3000. 


238  LESSONS   IN  ASTRONOMY 

For  some  reason,  the  fourth  satellite  is  a  very  dark-complexioned 
body,  so  that  when  it  crosses  the  planet's  disk  it  is  hardly  distin- 
guishable from  its  own  shadow;  the  others  under  similar  circum- 
stances appear  bright,  dark,  or  invisible,  according  to  the  brightness 
of  the  background.  In  the  case  of  the  fourth  satellite  a  certain  reg- 
ular change  of  brightness  suggests  that  it  probably  follows  the  exam- 
ple of  our  moon  in  always  keeping  the  same  face  towards  the  planet, 
and  Douglass  from  the  Flagstaff  Observatory,  in  1897,  announced  a 
similar  behavior  of  the  third.  The  other  satellites  are  very  faint. 
The  fifth  is  nearest  of  all  to  the  planet,  being  only  112,500  miles 
from  its  center.  The  sixth  and  seventh  seem  to  be  tiny  twin  satel- 
lites, moving  in  orbits  that  are  nearly  equal  and  "interlocked," 
7,500,000  miles  from  the  planet.  The  eighth  was  discovered  by 
Melotte  in  1908  on  photographs  made  at  Greenwich  for  the  sixth 
and  seventh,  and  a  ninth  was  found  by  Nicholson  at  the  Lick  Observ- 
atory in  1914.  These  two  are  another  pair  of  twins,  twice  as  far 
from  Jupiter  as  the  sixth  and  seventh,  and  revolving  in  the  opposite 
direction. 

273,  Eclipses  and  Transits. — The  orbits  of  the  satellites 
are  so  nearly  in  the  plane  of  the  planet's  orbit  that  with 
the  exception  of  the  fourth,  which  escapes  about  half  the 
time,  they  are  eclipsed  at  every  revolution.  Ordinarily 
we  see  only  the  beginning  or  the  end  of  an  eclipse ;  but 
when  the  planet  is  very  near  quadrature  the  shadow  pro- 
jects so  far  to  one  side  that  the  whole  eclipse  of  every 
satellite,  except  the  first,  takes  place  clear  of  the  disk, 
and  both  the  disappearance  and  reappearance  can  be 
observed.  At  opposition  neither  is  visible. 

Two  important  uses  have  been  made  of  these  eclipses : 
they  have  been  employed  for  the  determination  of  longi- 
tude, and  they  furnish  the  means  of  ascertaining  the  time 
required  by  light  to  traverse  the  space  between  the  earth  and 
the  sun.  (See  Appendix,  Sees.  431-434.) 


SATURN  239 

SATURN 

274.  This  is  the  most  remote  of  the  planets  known  to 
the  ancients.     It  appears  as  a  star  of  the  first  magnitude 
(outshining    all   of  them,  indeed,   except  Sirius)   with  a 
steady,  yellowish  light,  not  varying  much  in  appearance 
from  month  to   month,  though   in  the   course   of  fifteen 
years  it  alternately  gains  and  loses  nearly  fifty  per  cent 
of  its  brightness  with  the  changing  phases  of  its  rings; 
for  it  is  unique  among  the  heavenly  bodies,  a  great  globe 
attended  by  nine1  satellites  and  surrounded  by  a  system  of 
rings  which  has  no  counterpart  elsewhere  in  the  universe, 
so  far  as  known. 

Its  mean  distance  from  the  sun  is  about  9J  astronomical 
units,  or  886,000000  miles;  but  the  distance  varies  over 
100,000000  miles  on  account  of  the  considerable  eccen- 
tricity of  the  orbit  (0.056).  Its  least  distance  from  the 
earth  is  about  774,000000  miles,  the  greatest  about 
1028,000000.  The  inclination  of  the  orbit  to  the  ecliptic 
is  2J°.  The  sidereal  period  is  about  29£  years,  the  synodic 
period  being  378  days,  or  nearly  a  year  and  a  fortnight. 

275,  Dimensions,    Mass,    etc.  —  The    apparent    mean 
diameter  of  the  planet  varies  according  to  the  distance, 
from  14"  to  20".     The  planet  is  more  flattened  at  the 
poles  than  any  other  (nearly  -Jj),  so  that  while  the  equa- 
torial diameter  is  about  76,000  miles,  the  polar  is  only 
70,000 ;  the  mean  diameter   (Sec.  112)   being  not   quite 
74,000,  —  a  little  more  than  nine  times  that  of  the  earth. 
Its  surface  is  about  84  times  that  of  the  earth,  and  its 
volume  770  times.     Its  mass  is  found  (by  means  of  its 

1  The  presence  of  a  tenth  has  been  suspected,  but  not  fully  confirmed. 


240  LESSONS  IN  ASTRONOMY 

satellites)  to  be  95  times  that  of  the  earth,  so  that  its 
mean  density  comes  out  only  one-eighth  that  of  the  earth, 
—  actually  less  than  that  of  water  !  It  is  by  far  the  least 
dense  of  all  the  planetary  family. 

Its  mean  superficial  gravity  is  about  1.2  times  as  great 
as  gravity  upon  the  earth,  varying,  however,  nearly  twenty- 
five  per  cent  between  the  equator  and  the  pole,  so  that  at 
the  planet's  equator  it  is  practically  the  same  as  upon  the 
earth.  It  rotates  on  its  axis  in  about  10h14m ,  but  different 
spots  give  various  results,  as  in  the  case  of  Jupiter. 

The  equator  of  the  planet  is  inclined  about  27°  to  the 
plane  of  its  orbit  —  about  28°  to  the  ecliptic. 

276.  Surface,    Albedo,    Spectrum.  —  The   disk   of  the 
planet,  like  that  of  Jupiter,  is  shaded  at  the  edge,  and,  like 
Jupiter,  it  shows  a  number  of  belts  arranged  parallel  to 
the  equator.     The  equatorial  belt  is  very  bright,  and  is 
often  of  a  delicate  pinkish  tinge.     The  belts  in  higher 
latitudes  are  comparatively  faint  and  narrow,  while  just  at 
the  pole  there  is  usually  a  cap  of  olive  green  (see  Fig.  65). 

Zollner  makes  the  mean  albedo  of  the  planet  0.52,  about 
the  same  as  that  of  Venus. 

The  planet's  spectrum  is  substantially  like  that  of 
Jupiter,  but  the  dark  bands  are  more  pronounced.  These 
bands,  however,  do  not  appear  in  the  spectrum  of  the  ring, 
which  probably  has  very  little  atmosphere.  As  to  its  phys- 
ical condition  and  constitution,  the  planet  is  probably  much 
like  Jupiter,  though  it  does  not  seem  to  be  "boiling" 
quite  so  vigorously. 

277.  The  Rings.  —  The  most  remarkable  peculiarity  of 
the  planet  is  its  ring  system.     The  globe  is  surrounded  by 
three  thin,  flat,  concentric   rings,  like  circular  disks  of 


FIG.  65.  —  Saturn 
After  Proctor 


241 


242  LESSONS  IN  ASTRONOMY 

paper  pierced  through  the  center.     They  are  generally 
referred  to  as  A,  B,  and  (7,  A  being  the  exterior  one. 

Galileo  half  discovered  them  in  1610  ;  i.e.,  he  saw  with  his  little 
telescope  two  appendages,  one  on  each  side  of  the  planet ;  but  he 
could  make  nothing  of  them,  and  after  a  while  he  lost  them.  The 
problem  remained  unsolved  for  nearly  fifty  years,  until  Huyghens 
explained  the  mystery  in  1655.  Twenty  years  later  D.  Cassini  dis- 
covered that  the  ring  is  double,  i.e.,  composed  of  two  concentric 
rings,  with  a  dark  line  of  separation  between  them,  and  in  1850, 
Bond  of  Cambridge  (U.S.)  discovered  the  third  "  dusky  "  or  "  gauze  " 
ring  between  the  principal  ring  and  the  planet.  (It  was  discovered 
a  fortnight  later,  independently,  by  Dawes  in  England.) 

The  outer  ring,  J,  has  a  diameter  of  about  173,000 
miles  and  a  width  of  about  11,000.  Cassini's  division  is 
about  2000  miles  wide ;  the  ring  J5,  which  is  much  the 
broadest  of  the  three,  is  about  18,000.  The  semi-transpar- 
ent ring,  (7,  has  a  width  of  about  11,000  miles,  leaving  a 
clear  space  of  very  nearly  6000  miles  in  width  between 
the  planet's  equator  and  its  inner  edge.  The  thickness  of 
the  rings  is  extremely  small,  —  probably  not  over  50  miles, 
as  proved  by  the  appearance  presented  when  once  in  15 
years  we  view  them  edgewise. 

The  recent  researches  of  H.  Struve  show  that  the 
mass  of  the  rings  and  their  mean  density  are  also  sur- 
prisingly small,  —  so  small  that  the  rings  exert  hardly 
more  influence  on  the  motion  of  the  satellites  than  if  they 
were  composed  of  "  immaterial  light,"  to  use  his  own  expres- 
sion. A  very  recent  discussion  by  Professor  Hall  indi- 
cates, however,  that  the  mass,  though  certainly  extremely 
small,  is  by  no  means  insensible,  being  about  yyVo  °f  the 
planet's  mass,  and  about  two  thirds  that  of  Titan,  the 
largest  satellite. 


SATURN  243 

278.  Phases  of  the  Rings.  —  The  plane  of  the  rings 
coincides  with  the  plane  of  the  planet's  equator,  and  is 
inclined  about  28°  to  the  ecliptic.  It,  of  course,  remains 
parallel  to  itself  at  all  times.  Twice  in  a  revolution  of 
the  planet,  therefore,  this  plane  sweeps  across  the  orbit 
of  the  earth  (too  small  to  be  shown  in  Fig.  66),  occu- 
pying nearly  a  year  in  so  doing ;  and  whenever  the  plane 
passes  between  the  earth  and  the  sun  the  dark  side  of 
the  ring  is  towards  us  and  the  edge  alone  is  visible, 


FIG.  66.  —The  Phases  of  Saturn's  Rings 

as  when  the  planet  is  at  1  or  2 ;  when  it  is  at  the  inter- 
mediate points,  3  and  4,  the  rings  present  their  widest 
opening. 

When  the  ring  is  exactly  edgewise  towards  us,  only  the  largest 
telescopes  can  see  it,  like  a  fine  needle  of  light  piercing  the  planet's 
ball,  as  in  the  uppermost  engraving  of  Fig.  65.  It  becomes  obvious 
at  such  times  that  the  thickness  of  the  rings  is  not  uniform,  since 
considerable  irregularities  appear  upon  the  line  of  light  at  different 
points.  The  last  period  of  disappearance  was  in  1907. 


244  LESSONS  IN  ASTRONOMY 

279.  Structure  of  the  Rings.  —  It  is   now  universally 
admitted  that  they  are  not  continuous  sheets,  either  solid 
or  liquid,  but  mere  swarms  of  separate  particles,  each  par- 
ticle pursuing  its  own  independent  orbit  around  the  planet, 
though  all  moving  nearly  in  a  common  plane. 

The  idea  was  first  suggested  by  J.  Cassini  in  1715,  but  was  lost 
sight  of  until  again  brought  into  notice  by  Bond  in  1850.  A  little 
later  Peirce  proved  from  mechanical  considerations  that  the  rings 
could  not  be  solid;  and  not  long  after,  Maxwell  showed  that  they 
could  not  be  "  continuous  sheets  "  of  any  kind,  either  solid  or  liquid, 
but  might  be  composed  of  separate  particles  moving  independently. 
More  recently  Miiller  and  Seeliger  have  shown  from  photometric 
observations  that  the  variations  in  the  brightness  of  the  ring  corre- 
spond to  this  "meteoric  theory"  ;  and  still  more  recently  (in  1895) 
Keeler  demonstrated,  by  a  most  beautiful  and  delicate  spectroscopic 
observation,  that  the  outer  edge  of  the  ring  in  its  rotation  really 
moves  more  slowly  than  the  inner,  just  as  the  theory  requires. 

It  remains  uncertain  whether  the  rings  constitute  a  system  that 
is  permanently  stable,  or  whether  they  are  liable  ultimately  to  be 
broken  up  and  disappear. 

280.  Satellites. — Saturn  has  nine1  of  these  attendants. 
Titan,  the  largest,  was  discovered  by  Huyghens  in  1655. 
It  looks  like  a  star  of  the  ninth  magnitude,  and  is  easily 
seen  with  a  three-inch  telescope.    Tethys,  Dione,  and  Rhea 
are  fainter  and  closer  to  the  bright  planet.     They  can  be 
seen  with  a  five-inch  telescope,  as  can  the  more  distant 
lapetus.     All  the  others  are  very  faint. 

Since  the  order  of  discovery  does  not  agree  with  that  of  distance, 
it  has  been  found  convenient  to  designate  them  by  the  names 
assigned  by  Sir  John  Herschel,  as  follows,  beginning  with  the  most 
remote,  viz. :  lapfitus,  (Hyperion),  Titan,  Rhea,  Dione,  Tethys ; 
Enoeladus,  Mimas.  (The  name  Hyperion  was  not  given  by  Herschel, 
but  interpolated  after  its  discovery  by  Bond.) 

1  See  footnote  on  page  239. 


URANUS  245 

The  range  of  the  system  is  enormous.  lapetus  has  a  distance  of 
2,225000  miles,  with  a  period  of  79  days,  —  nearly  as  long  as  that  of 
Mercury.  On  the  western  side  of  the  planet  this  satellite  is  always 
much  brighter  than  upon  the  eastern,  showing  that,  like  our  own 
moon,  it  keeps  the  same  face  towards  its  primary. 

Titan,  as  its  name  suggests,  is  by  far  the  largest.  Its  distance  is 
about  770,000  miles  and  its  period  a  little  less  than  16  days.  It  is 
probably  3000  or  4000  miles  in  diameter,  and,  according  to  Stone, 
its  mass  is  •%•$•-$•$  of  Saturn's,  or  about  double  that  of  our  moon. 
The  orbit  of  lapetus  is  inclined  nearly  10°  to  the  plane  of  the 
rings,  but  all  of  the  other  satellites  move  almost  exactly  in  their 
plane,  and  all  the  five  inner  ones  in  orbits  nearly  circular.  In  1899 
W.  H.  Pickering  announced  the  discovery  of  an  extremely  small 
ninth  satellite  on  photographs  made  at  Arequipa  the  preceding  year. 
The  data  were  then  insufficient  to  determine  its  orbit :  but  the  dis- 
covery has  since  been  fully  confirmed,  and  the  distance  of  the  satel- 
lite (Phoebe)  from  Saturn  is  found  to  be  8,000000  miles,  its  period  18 
months,  its  motion  apparently  retrograde,  and  its  diameter  about  200 
miles. 

URANUS 

281.  Uranus  (not  U-ra/nus)  was  the  first  planet  ever 
"  discovered,"  and  the  discovery  created  great  excitement 
and  brought  the  highest  honors  to  the  astronomer.  It  was 
found  accidentally  by  the  elder  Herschel  on  March  13, 
1781,  while  "sweeping"  for  interesting  objects  with  a 
seven-inch  reflector  of  his  own  construction.  He  recog- 
nized it  at  once  by  its  disk  as  something  different  from  a 
star,  but  supposed  it  to  be  a  peculiar  sort  of  comet,  and 
its  planetary  character  was  not  demonstrated  until  nearly 
a  year  had  passed.  It  is  easily  visible  to  a  good  eye  as 
a  star  of  the  sixth  magnitude. 

Its  mean  distance  from  the  sun  is  about  19  times  that  of 
the  earth,  or  about  1800,000000  miles,  and  the  eccentricity 


246  LESSONS  IN  ASTRONOMY 

of  its  orbit  is  about  the  same  as  that  of  Jupiter's.  The 
inclination  of  the  orbit  to  the  ecliptic  is  very  slight,  — 
only  46'.  The  sidereal  period  is  84  years,  and  the  synodic 
3691  days. 

In  the  telescope  it  shows  a  greenish  disk  about  4"  in 
diameter,  which  corresponds  to  a  real  diameter  of  about 
30,000  miles.  This  makes  its  bulk  about  54  times  that 
of  the  earth.  The  planet's  mass  is  found  from  its  satel- 
lites to  be  about  14.6  times  that  of  the  earth ;  its  density, 
therefore,  is  0.27, — about  the  same  as  that  of  Jupiter  and 
the  sun. 

The  albedo  of  the  planet,  according  to  Zollner,  is  very 
high,  0.64,  —  even  a  little  above  that  of  Jupiter.  The 
spectrum  exhibits  intense  dark  bands  in  the  red,  due  to 
some  unidentified  substance  in  the  planet's  atmosphere. 
These  bands  explain  the  marked  greenish  tint  of  the 
planet's  light.  The  atmosphere  is  probably  dense. 

The  disk  is  obviously  oval,  with  an  ellipticity  of  about 
•j*?.  There  are  no  clear  markings  upon  it,  but  there  seem 
to  be  faint  traces  of  something  like  belts.  No  spots  are 
visible  from  which  to  determine  the  planet's  diurnal 
rotation.  Probably,  however,  it  is  rapid.1 

282.  Satellites.  —  The  planet  has  four  satellites,— 
Ariel,  Umbriel,  Titania,  and  Oberon,  Ariel  being  the 
nearest  to  the  planet. 

The  two  brightest,  Oberon  and  Titania,  were  discovered  by  Sir 
William  Herschel  a  few  years  after  his  discovery  of  the  planet ;  Ariel 
and  Umbriel,  by  Lassell  in  1851. 

1  A  period  of  10h50m  was  found  with  the  spectroscope  at  the  Lowell 
Observatory  in  1912,  the  direction  of  rotation  corresponding  to  that  of 
the  revolution  of  the  satellites. 


NEPTUNE  247 

They  are  among  the  smallest  bodies  in  the  solar  system, 
visible  only  in  the  largest  telescopes. 

Their  orbits  are  sensibly  circular,  and  all  lie  in  one 
plane,  which  ought  to  be,  and  probably  is,  coincident  with 
the  plane  of  the  planet's  equator. 

They  are  very  close  packed  also,  Oberon  having  a  distance  of  only 
375,000  miles  and  a  period  of  13dllh,  while  Ariel  has  a  period  of 
2d12h  at  a  distance  of  120,000  miles.  Titania,  the  largest  and 
brightest  of  them,  has  a  distance  of  280,000  miles,  somewhat 
greater  than  that  of  the  moon  from  the  earth,  with  a  period  of 


The  most  remarkable  thing  about  this  system  remains  to 
be  mentioned.  The  plane  of  their  orbits  is  inclined  82°.2, 
or  almost  perpendicularly,  to  the  plane  of  the  ecliptic,  and 
in  that  plane  they  revolve  backwards. 


NEPTUNE 

283.  Discovery.  —  The  discovery  of  this  planet  is  con- 
sidered the  greatest  triumph  of  mathematical  astronomy. 
Uranus  failed  to  move  precisely  in  the  path  computed  for 
it,  and  was  misguided  by  some  unknown  influence  to  an 
extent  which  could  almost  be  seen  with  the  naked  eye. 
The  difference  between  the  actual  and  computed  places  in 
1845  was  the  "  intolerable  quantity  "  of  nearly  two  minutes 
of  arc. 

This  is  a  little  more  than  half  the  distance  between  the  two  prin- 
cipal components  of  the  double-double  star,  Epsilon  Lyrse,  the  north- 
ern one  of  the  two  little  stars  which  form  the  small  equilateral 
triangle  with  Vega  (Sees.  67  and  375).  A  very  sharp  eye  detects 
the  duplicity  of  Epsilon  without  the  aid  of  a  telescope. 


248  LESSONS  IN  ASTRONOMY 

One  might  think  that  such  a  minute  discrepancy  between 
observation  and  theory  was  hardly  worth  minding,  and  that 
to  consider  it  "intolerable"  was  putting  the  case  very 
strongly.  But  just  these  minute  discrepancies  supplied 
the  data  which  were  found  sufficient  for  calculating  the 
position  of  a  great  unknown  world,  and  bringing  it  to 
light.  As  the  result  of  a  most  skillful  and  laborious  inves- 
tigation, Leverrier  (born  1811,  died  1877)  wrote  to  Galle1 
in  substance : 

"  Direct  your  telescope  to  a  point  on  the  ecliptic  in  the  constella- 
tion of  Aquarius,  in  longitude  326°,  and  you  will  find  within  a  degree 
of  that  place  a  new  planet,  looking  like  a  star  of  about  the  ninth 
magnitude,  and  having  a  perceptible  disk." 

The  planet  was  found  at  Berlin  on  the  night  of  Sept.  23, 
1846,  in  exact  accordance  with  this  prediction,  within 
half  an  hour  after  the  astronomers  began  looking  for  it 
and  within  52'  of  the  precise  point  that  Leverrier  had 
indicated. 

We  cannot  here  take  the  space  for  an  historical  statement,  further 
than  to  say  that  the  English  Adams  fairly  divides  with  Leverrier  the 
credit  for  the  mathematical  discovery  of  the  planet,  having  solved 
the  problem  and  deduced  the  planet's  approximate  place  even  earlier 
than  his  competitor.  The  planet 'was  being  searched  for  in  England 
at  the  time  it  was  found  in  Germany.  In  fact,  it  had  already  been 
observed,  and  the  discovery  would  necessarily  have  followed  in  a  few 
weeks,  upon  the  reduction  of  the  observations. 

284.  Error  of  the  Computed  Orbit.  —  Both  Adams  and  Leverrier, 
besides  calculating  the  planet's  position  in  the  sky,  had  deduced  ele- 
ments of  its  orbit  and  a  value  for  its  mass,  which  turned  out  to  be 

1  Galle,  long  director  of  the  observatory  at  Breslau,  died  in  1910,  at 
the  advanced  age  of  ninety-eight  years. 


NEPTUNE  249 

seriously  wrong,  and  certain  high  authorities  have  therefore  charac- 
terized the  discovery  as  a  "happy  accident."  This  is  not  so,  how- 
ever. While  the  data  and  methods  employed  were  not  sufficient 
to  determine  the  planet's  orbit  with  accuracy,  they  were  adequate 
to  ascertain  the  planet's  direction  from  the  earth.  The  computers 
informed  the  observers  where  to  point  their  telescopes,  and  this  was  all 
that  was  necessary  for  finding  the  planet. 

285.  JThe  Planet  and  its  Orbit The  planet's  mean  dis- 
tance from  the  sun  is  a  little  less  than  2800,000000  miles 
(800,000000  miles  nearer  the  sun  than  it  should  be  accord- 
ing to  B ode's  law).  The  orbit  is  very  nearly  circular,  its 
eccentricity  being  only  0.009.  The  inclination  of  the  orbit 
is  about  1|°.  The  period  of  the  planet  is  about  164  years 
(instead  of  217,  as  it  should  have  been  according  to  Lever- 
rier's  computed  orbit)  and  the  orbital  velocity  is  about 
3£  miles  per  second. 

Neptune  appears  in  the  telescope  as  a  small  star  of 
between  the  eighth  and  ninth  magnitudes,  absolutely 
invisible  to  the  naked  eye,  though  easily  seen  with  a 
good  opera-glass.  Like  Uranus,  it  shows  a  greenish  disk, 
having  an  apparent  diameter  of  about  2".6.  The  real 
diameter  of  the  planet  is  about  35,000  miles,  according  to 
the  "American  Ephemeris,"  which  makes  its  volume  about 
86  times  that  of  the  earth. 

Its  mass,  as  determined  by  means  of  its  satellite,  is  about 
18  times  that  of  the  earth,  and  its  density  about  0.20. 

The  planet's   albedo,   according  to   Zollner,  is   0.46,  — 
a  trifle  less  than  that  of  Saturn  and  Venus. 

There  are  no  visible  markings  upon  its  surface,  and 
nothing  certain  is  known  as  to  its  rotation. 


250  LESSONS  IN  ASTRONOMY 

The  spectrum  of  the  planet  appears  to  be  like  that  of 
Uranus,  but  of  course  is  rather  faint. 

It  will  be  noticed  that  Uranus  and  Neptune  form  a  "pair  of 
twins,"  very  much  as  the  earth  and  Venus  do,  being  almost  alike  in 
magnitude,  density,  and  many  other  characteristics. 

286.  Satellite.  —  Neptune  has  one  satellite,  discovered 
by  Lassell  within  a  month  after  the  discovery  of  the  planet 
itself.     Its  distance  is  about  222,000  miles,  and  its  period 
5d21h.     Its  orbit  is  inclined  to  the  ecliptic  at  an  angle  of 
34°  48',  and  it  moves  backward  in  it  from  east  to  westr 
like  the  satellites  of  Uranus.     From  its  brightness,  as  com- 
pared with  that  of  Neptune  itself,  its  diameter  is  estimated 
as  about  the  same  as  that  of  our  own  moon. 

287.  The  Solar  System  as  seen  from  Neptune.  —  At 
Neptune's  distance  the  sun  itself  has  an  apparent  diam- 
eter of  only  a  little  more  than  one  minute  of  arc,  —  about 
the  diameter  of  Venus  when  nearest  us,  and  top  small  to 
be  seen  as  a  disk  by  the  naked  eye,  if  there  are  eyes  on 
Neptune.     The  solar  light  and  heat  there  are  only  -g^  of 
what  we  get  at  the  earth. 

Still,  we  must  not  imagine  that  the  Neptunian  sunlight 
is  feeble  as  compared  with  starlight,  or  even  moonlight. 
Even  at  the  distance  of  Neptune  the  sun  gives  a  light 
nearly  equal  to  700  full  moons.  This  is  about  80  times 
the  light  of  a  standard  candle  at  one  meter's  distance,  and 
is  abundant  for  all  visual  purposes.  In  fact,  as  seen  from 
Neptune,  the  sun  would  look  very  like  a  large  electric  arc 
lamp  at  a  distance  of  a  few  yards. 

288.  Ultra-Neptunian  Planets.  —  Perhaps  the  breaking  down  of 
Bode's  law  at  Neptune  may  be  regarded  as  an  indication  that  the 


STABILITY  OF    SOLAR   SYSTEM  251 

solar  system  terminates  there,  and  that  there  is  no  remoter  planet; 
but  of  course  it  does  not  make  it  certain.  If  such  a  planet  exists,  it 
is  sure  to  be  found  sooner  or  later,  either  by  means  of  the  disturb- 
ances it  produces  in  the  motion  of  Uranus  and  Neptune,  or  else  by 
the  methods  of  the  asteroid  hunters,  —  although  its  slow  motion  will 
render  its  discovery  in  that  way  difficult.  Quite  possibly  such  a  dis- 
covery may  come  within  a  few  years  as  a  result  of  the  photographic 
star -charting  operations  now  in  progress. 

288*.  Stability  of  the  Solar  System.  —  It  is  an  interesting  and 
important  question,  once  long  and  warmly  discussed,  whether  the 
so-called  "perturbations,"  which  result  from  the  mutual  attractions 
of  the  planets,  can  ever  seriously  derange  the  system.  It  is  now 
nearly  a  century  since  Laplace  and  Lagrange  were  supposed  to  have 
demonstrated  that  they  cannot ;  that  the  system  is  stable  in  itself, 
all  the  disturbances  due  to  gravitation  being  either  of  such  a  charac- 
ter, or  so  limited  in  extent,  that  they  can  never  produce  any  seriously 
harmful  effects  upon  the  earth  or  any  of  the  larger  planets.  But  the 
recent  work  of  mathematicians  has  proved  that  this  sweeping  conclu- 
sion is  unwarranted.  The  system  is  secure  for  thousands,  perhaps 
for  millions,  of  years  ;  perhaps  forever ;  but  it  is  not  yet  demonstrated 
that  in  some  remote  future  the  accumulated  perturbations  may  not 
result  in  disaster. 

Moreover,  besides  gravitational  disturbances,  there  are  other  causes 
which  may  work  destructively.  Many  such  are  conceivable,  —  such, 
for  instance,  as  the  retardation  of  the  speed  of  the  planets,  which 
would  be  caused  by  the  presence  of  a  resisting  medium  in  space,  or 
by  the  encounter  of  the  system  with  a  sufficiently  dense  and  extended 
cloud  of  meteors. 

But  so  far  as  we  can  now  judge,  the  ultimate  cooling  of  the  sun 
(Sec.  193)  is  likely  to  extinguish  life  upon  the  planets  long  before 
the  mechanical  destruction  of  the  system  can  occur. 

NOTE.  —  The  values  given  in  Table  II  of  the  Appendix  are  allowed  to 
stand  as  in  former  editions,  in  order  that  their  comparison  with  those 
given  in  the  text  may  illustrate  to  the  student  the  measure  of  uncertainty 
that  still  remains  in  such  astronomical  data. 


CHAPTER  X 

COMETS   AND   METEORS 

The  Number,  Designation,  and  Orbits  of  Comets  — Their  Constituent  Parts 
and  Appearance  —  Their  Spectra  and  Physical  Constitution  —  Their  Prob- 
able Origin  — Remarkable  Comets  —  Photography  of  Comets— Aerolites, 
their  Fall  and  Characteristics  —  Shooting-Stars,  Meteoric  Showers— Con- 
nection between  Comets  and  Meteors 

COMETS 

289.  Comets,  their  Appearance  and  Number.  —  The 
word  " comet "  (derived  from  the  Greek  kome)  means  a 
"  hairy  star."  The  appearance  is  that  of  a  rounded  cloud 
of  luminous  fog  with  a  star  shining  through  it,  often 
accompanied  by  a  long  fan-shaped  train,  or  "  tail,"  of  hazy 
light.  They  present  themselves  from  time  to  time  in  the 
heavens,  mostly  when  unexpected,  move  across  the  con- 
stellations in  a  path  longer  or  shorter  according  to  circum- 
stances, and  remain  visible  for  some  weeks  or  months 
until  they  fade  out  and  vanish  in  the  distance.  The  large 
ones  are  magnificent  objects,  sometimes  as  bright  as  Venus 
and  visible  by  day,  with  a  head  as  large  as  the  moon,  and 
having  a  train  which  extends  from  the  horizon  to  the 
zenith,  and  is  really  long  enough  to  reach  from  the  earth 
to  the  sun.  Such  comets  are  rare,  however ;  the  majority 
are  faint  wisps  of  light,  visible  only  with  the  telescope. 
Fig.  67  is  a  representation  of  Donati's  comet  of  1858, 
which  was  one  of  the  finest  ever  seen. 

252 


FIG.  67.  — Naked-Eye  View  of  Donati's  Comet,  Oct.  4,  1858 
Bond 


253 


254  LESSONS  IN  ASTRONOMY 

In  ancient  times  comets  were  always  regarded  with  terror,  as  at 
least  presaging  evil,  if  not  actively  malignant,  and  the  notion  still 
survives  in  certain  quarters,  though  the  most  careful  research  goes 
to  prove  that  they  exert  upon  the  earth  not  the  slightest  perceptible 
influence  of  any  kind. 

Thus  far,  up  to  the  beginning  of  the  new  century,  our 
lists  contain  800  recorded  appearances,  not  all,  however, 
of  different  comets,  for  some  (periodic)  have  been  counted 
several  times.  About  400  were  observed  before  .the  inven- 
tion of  the  telescope  in  1609,  and  therefore  must  have 
been  fairly  bright.  Of  those  observed  since  then,  only  a 
small  proportion  have  been  conspicuous  to  the  naked  eye,  — 
perhaps  one  in  five.  The  total  number  that  visit  the  solar 
system  must  be  enormous ;  for  there  is  seldom  a  time 
when  one  at  least  is  not  in  sight,  and  even  with  the  tele- 
scope we  see  only  the  few  which  come  near  the  earth  and 
are  favorably  situated  for  observation. 

290.  Designation  of  Comets.  —  A  remarkable  comet  gen- 
erally bears  the  name  of  its  discoverer  or  of  some  one  who 
has  "  acquired  its  ownership,"  so  to  speak,  by  some  impor- 
tant research  concerning  it.  Thus  we  have  Halley's, 
Encke's,  and  Donati's  comets.  The  ordinary  telescopic 
comets  are  designated  only  by  the  year  of  discovery,  with 
a  letter  indicating  the  order  of  discovery  in  that  year,  as 
comet  "  a,  1890  "  (the  letter  preceding  the  year) ;  or,  still 
again,  with  the  year  and  a  Roman  numeral  following  and 
denoting  the  order  of  perihelion  passage,  as  1890-1,  the 
latter  method  being  the  most  used.  In  some  cases  a  comet 
bears  a  double  name,  as  the  Lexell-Brooks  comet  (1889-V), 
which  was  investigated  by  Lexell  in  1770,  and  discovered 
by  Brooks  on  its  recent  return  in  1889, 


COMETS  255 

291.  Duration  of  Visibility  and  Brightness.  —  The  great 
comet  of  1811  was  observed  for  seventeen  months,  and 
the  little   comet,   known  as  1889-1,   for  more  than  two 
years,  —  the  longest  period  of  visibility  on  record.     On 
the  other  hand,  the  whole*  appearance  sometimes  lasts  only 
a  week  or  two.     The  average  is  probably  not  far  from 
three  •  months. 

As  to  brightness,  comets  differ  widely.  About  one  in 
five  reaches  the  naked-eye  limit,  and  a  very  few,  say  four 
or  five  in  a  century,  are  bright  enough  to  be  seen  in  the 
daytime.  The  great  comet  of  1882  and  comet  a,  1910, 
were  the  last  ones  so  visible. 

292.  Their  Orbits.  —  A  large  majority  of  the  comets  move 
in  orbits  that  are  sensibly  parabolas.     (See  Appendix,  Sees. 
439-440.)     A  comet  moving  in  such  an  orbit  approaches 
'the  sun  from  an  enormous  distance,  far  beyond  the  limits 
of  the  solar  system,  sweeps  once  around  the  sun,  and  goes 
off,  never  to  come  back.     The  parabola  does  not  return 
into  itself  and  form  a  closed  curve,  like  the  circle  and 
ellipse,  but  recedes  to  infinity.     Of  the  nearly  400  orbits 
that  have  been  computed,  more  than  300  appear  to  be  of 
this  kind.     About  85   orbits  are  more  or  less  distinctly 
elliptical,  and  about  half  a  dozen  are  perhaps  hyperbolas 
(see  Appendix,   Sec.   440);  but  the   hyperbolas  differ  so 
slightly  from  parabolas  that  the  hyperbolic  character  is  not 
really  certain  in  a  single  case. 

Comets  which  have  elliptical  orbits  of  course  return  at 
regular  intervals.  Of  the  apparently  elliptical  orbits, 
there  are  about  a  dozen  to  which  computation  assigns 
periods  near  to  or  exceeding  1000  years.  These  orbits 
approach  parabolas  so  closely  that  their  real  character  is 


256 


LESSONS  IN  ASTRONOMY 


still  rather  doubtful.  About  75  comets,  however,  have 
orbits  which  are  distinctly  and  certainly  elliptical,  and 
60  have  periods  of  less  than  one  hundred  years.  About 
20  of  these  have  been  actually  observed  at  two  or  more 
returns  to  perihelion.  As  to  the  rest  of  them,  some  are 
now  due  within  a  few  years,  and  some  have  probably  been 
lost  to  observation,  either  like  Biela's  comet  (Sec.  312),  or 

by  having  their 
orbits  transformed 
by  perturbations. 

293.  The  first 
comet  ascertained  to 
move  in  an  elliptical 
orbit  was  that  known 
as  Halley's,  with  a 
period  of  about  sev-" 
enty-six  years,  its  peri- 
odicity having  been 
announced  by  Halley 
in  1705.  It.  has  since 
been  observed  in  1759 
and  1835  and  at  its 
last  return  in  1909  and 
1910.  The  second  of 
the  periodic  comets 
(in  the  order  of  dis- 
covery) is  Encke's,  with  the  shortest  period  known,  —  only  three  and 
one-half  years.  Its  periodicity  was  discovered  in  1819,  though  the 
comet  itself  had  been  observed  several  times  before.  Fig.  68  shows 
the  orbits  of  a  number  of  short-period  comets  (it  would  cause  confu- 
sion to  insert  more  of  them)  and  also  a  part  of  the  orbit  of  Halley's 
comet.  These  comets  all  have  periods  ranging  from  three  and  one- 
half  to  eight  years,  and  it  will  be  noticed  that  they  all  pass  very  near 
to  the  orbit  of  Jupiter.  Moreover,  each  comet's  orbit  crosses  that  of 


FIG.  68.  —  Orbits  of  Short-Period  Comets 


ORBITS  OF  COMETS  257 

Jupiter  near  one  of  its  nodes,  the  node  being  marked  by  a  short  cross 
line  on  the  comet's  orbit.  The  fact  is  very  significant,  showing  that 
these  comets  at  times  come  very  near  to  Jupiter,  and  it  points  to  an 
almost  certain  connection  between  that  planet  and  these  bodies. 

294.  Comet-Groups.  —  There  are  several  instances  in  which  a 
number  of  comets,  certainly  distinct,  chase  each  other  along  almost 
exactly  the  same  path,  at  an  interval  usually  of  a  few  months  or 
years,  though  they  sometimes  appear  simultaneously.     The  most 
remarkable  of  these  "  comet-groups  "  is  that  composed  of  the  great 
comets  of  1668,  1843,  1880,  1882,  and  1887.     It  is,  of  course,  nearly 
certain  that  the  comets  of  such  a  "  group  "  have  a  common  origin. 

295.  Perihelion  Distance,  etc.  — Eight  of  the  300  come- 
tary  orbits,  thus  far  determined,  approach  the  sun  within 
less  than   6,000000    miles,   and   four   have    a   perihelion 
distance  exceeding  200,000000.     A  single  comet  (that  of 
1729)  had  a  perihelion  distance  of  more  than  four  "astro- 
nomical units,"  or  375,000000  miles.     It  must  have  been 
an  enormous  one  to  be  visible  at  all  under  the  circum- 
stances.    There  may,  of  course,  be  any  number  of  comets 
with  still  greater  perihelion  distances,  because,  as  a  rule, 
we  are  able  to  see  only  such  as  come  reasonably  near  the 
earth,  and  this  is  probably  only  a  small  percentage  of  the 
total  number  that  visit  the  sun. 

The  inclinations  of  cometary  orbits  range  all  the  way 
from  zero  to  90°.  As  regards  the  direction  of  motion,  all 
the  elliptical  comets  having  periods  of  less  than  one 
hundred  years  move  direct,  i.e.,  from  west  to  east,  except 
Halley's  comet  and  Tempel's  comet  of  1866.  Other 
comets  show  no  decided  preponderance  either  way. 

296.  Parabolic  Comets  are  Visitors.  —  The  fact  that  the 
orbits  of  most  comets  are  sensibly  parabolic,  and  that  their 
planes  have  no  evident  relation  to  the  ecliptic,  indicates 


258  LESSONS  IN  ASTRONOMY 

(though  it  does  not  absolutely  prove)  that  these  bodies  do 
not  in  any  proper  sense  belong  to  the  solar  system,  but 
are  only  visitors.  Such  comets  come  to  us  precisely  as  if 
they  simply  dropped  towards  the  sun  from  an  enormous 
distance  among  the  stars ;  and  they  leave  the  system  with 
a  velocity  which,  if  no  force  but  the  sun's  attraction  acts 
upon  them,  will  carry  them  away  to  an  infinite  distance, 
or  until  they  encounter  the  attraction  of  some  other 
sun.  Their  motions  are  just  what  might  be  expected  of 
ponderable  masses  moving  among  the  stars  under  the 
law  of  gravitation. 

A  slightly  different  view  is  advocated  by  some  high  authorities, 
and  is  perhaps  more  probable,  —  that  these  comets  come  from  a  great 
distance  indeed,  but  not  from  among  the  stars.  It  may  be  that  our 
solar  system,  in  its  journey  through  space  (Sec.  342),  is  accompanied 
by  outlying  clouds  of  nebulous  matter,  and  that  these  are  the  source 
of  the  comets.  It  is  argued  that  if  this  were  not  the  case  the  number 
of  hyperbolic  orbits  would  be  much  greater,  because  we  should  meet 
so  many  more  comets  than  could  overtake  us. 

297.  Origin  of  Periodic  Comets But  while  the  para- 
bolic comets  are  thus  probably  strangers  and  visitors, 
there  is  a  question  as  to  the  periodic  comets  which  move 
in  elliptical  orbits.  Are  we  to  regard  them  as  native 
citizens,  or  only  as  naturalized  foreigners,  so  to  speak? 
It  is  evident  that,  somehow  or  other,  many  of  them  stand 
in  peculiar  relations  to  Jupiter,  Saturn,  and  other  planets, 
as  already  indicated  in  Sec.  293. 

All  short>period  comets  (those  which  have  periods  ran- 
ging from  three  to  eight  years)  pass  very  close  to  the  orbit 
of  Jupiter,  and  are  now  recognized  and  spoken  of  as  Jupi- 
ter's "  family  of  comets  " ;  more  than  twenty  are  known  at 


THE  CAPTURE  THEORY  259 

present.  Similarly,  Saturn  is  credited  with  two  comets, 
and  Uranus  with  two,  one  of  them  being  Tempel's  comet, 
which  is  closely  connected  with  the  November  meteors  and 
should  have  returned  in  1900,  but  was  not  seen.  Finally, 
Neptune  has  a  family  of  six  ;  among  them  Halley's  comet, 
and  two  others  which  have  returned  a  second  time  to 
perihelion  since  1880. 

298.  The  Capture  Theory The  generally  accepted 

theory  as  to  the  origin  of  these  "  comet-families  "  is  one 
first  suggested  by  Laplace  nearly  one  hundred  years  ago, — 
that  the  comets  which  compose  them  have  been  captured  by 
the  planet  to  which  they  stand  related.  A  comet  entering 
the  system  in  a  parabolic  orbit  and  passing  near  a  planet 
will  be  disturbed,  —  either  accelerated  or  retarded.  If  it 
is  accelerated,  it  is  easy  to  prove  that  the  original  para- 
bolic orbit  will  be  changed  to  an  hyperbola,  and  the 
comet  will  never  be  seen  again,  but  will  pass  out  of  the 
system  forever;  but  if  it  is  retarded,  the  orbit  becomes 
elliptical,  and  the  comet  will  revolve  around  the  sun  (not 
around  the  capturing  planet),  returning  at  each  successive 
revolution  to  the  place  where  it  was  first  disturbed. 

But  this  is  not  the  end.  After  a  certain  number  of 
revolutions,  the  planet  and  the  comet  will  come  together 
a  second  time  at  or  near  the  place  where  they  met  before. 
The  result  may  then  be  an  acceleration  which  will  send 
the  comet  out  of  the  system  finally  ;  but  it  is  an  even 
chance  at  least  that  it  may  be  a  second  retardation  and 
that  the  orbit  and  period  may  thus  be  further  diminished ; 
and  this  may  happen  over  and  over  again,  until  the  comet's 
orbit  falls  so  far  inside  that  of  the  planet  that  there  is  no 
further  disturbance  to  speak  of. 


260  LESSONS  IN  ASTRONOMY 

Given  time  enough  and  comets  enough,  and  the  result 
would  inevitably  be  such  a  comet-family  as  really  exists. 
Its  membership  can  hardly  be  permanent,  however  ;  sooner 
or  later,  if  not  first  disintegrated,  each  captured  comet  will 
almost  certainly  again  encounter  its  captor  under  such 
circumstances  as  to  be  thrown  out  of  the  system,  never 
to  return. 

299.  The  Lexell-Brooks  Comet —  The  "  capture  theory  " 
has  recently  received  an  interesting  illustration  in  the  case 
of  a  little  comet,  1889-V,  discovered  by  Mr.  Brooks  of 
Geneva,  N.Y.,  in  July,  1889.  It  was  soon  found  to  be 
moving  with  a  period  of  about  seven  years,  in  an  elliptical 
orbit  which  passes  very  near  to  that  of  Jupiter.  (We 
remark  in  passing  that  this  comet,  in  August,  divided  into 
four  fragments ;  see  Sec.  314.)  On  investigating  the  orbit 
more  carefully,  Dr.  S.  C.  Chandler  of  Cambridge  (U.S.) 
discovered  that,  in  1886,  the  comet  and  the  planet  had 
been  close  together  for  some  months,  and  that  as  a  conse- 
quence the  comet's  orbit  must  have  been  greatly  changed, 
the  previous  orbit  having  been  a  much  larger  one  with  a 
probable  period  of  nearly  twenty-seven  years. 

Now,  in  1770,  a  famous  comet  appeared,  which  was 
bright,  came  very  near  the  earth,  and,  according  to  Lexell's 
calculations,  was  then  moving  in  an  orbit  with  a  period  of 
only  five  and  a  half  years,  —  the  first  instance  of  a  short- 
period  comet  on  record  ;  but  it  was  never  seen  again.  The 
calculations  of  Laplace,  and  later  of  Leverrier,  showed  that, 
in  1779,  it  must  have  passed  very  near  to  Jupiter  and 
been  thrown  into  an  orbit  too  large  to  allow  it  to  be  seen 
from  the  earth  ;  also  that  the  period  might  probably  be 
about  twenty-seven  years.  This  would  bring  it  very  near 


CONSTITUTION  OF  COMETS  261 

to  Jupiter  again  in  1886,  and  it  was  natural,  therefore,  for 
Dr.  Chandler  to  infer  the  probable  identity  of  the  two 
comets,  —  a  conclusion  for  a  time  generally  accepted. 
Subsequent  calculations  by  Dr.  Charles  L.  Poor  of  Balti- 
more threw  doubt  upon  it,  however,  and  the  observations 
made  during  the  return  of  the  comet  in  1896  make  it  on 
the  whole  more  likely  that  Brooks's  comet  is  not  identical 
with  Lexell's,  but  very  probably  a  member  of  the  same 
comet-group  (Sec.  294).  Dr.  Poor  found  that  the  comet, 
in  1886,  passed  between  Jupiter  and  the  orbit  of  its  first 
satellite  within  about  200,000  miles  of  the  planet's  surface, 
which  accounts  for  its  separation  into  four  parts. 

PHYSICAL   CONSTITUTION  OF  COMETS 

300.  Constituent  Parts  of  a  Comet.  —  (a)  The  essential 
part  of  a  comet  —  that  which  is  always  present  and  gives 
the  comet  its  name — is  the  coma,  or  nebulosity,  a  hazy 
cloud  of  faintly  luminous  transparent  matter. 

(b)  Next,  we  have  the  nucleus,  which,  however,  is  want- 
ing in  many  comets,  and  makes  its  appearance  only  as  the 
comet  comes  near  the  sun.     It  is  a  bright,  more  or  less 
starlike    point  near  the   center  of  the  comet.     In   some 
cases  it  is  double,  or  even  multiple. 

(c)  The  tail,  or  train,  is  a  stream  of  light  which  com- 
monly accompanies  a  bright  comet  and  is  sometimes  pres- 
ent even  with  a  telescopic  one.     As  the  comet  approaches 
the  sun  the  tail  follows  it,  but  as  the  comet  moves  away 
from  the  sun  it  precedes.     It  is  always,  speaking  broadly, 
directed  away  from  the  sun,  though  its  precise  form  and 
position   are    determined   partly  by  the   comet's   motion. 


262  LESSONS  IN  ASTRONOMY 

It  is  practically  certain  that  it  consists  of  extremely  rarefied 
matter,  which  is  thrown  off  by  the  comet  and  powerfully 
repelled  by  the  sun. 

It  certainly  is  not  —  like  the  smoke  of  a  locomotive  or  train  of  a 
meteor  —  simply  left  behind  by  the  comet,  because  as  the  comet  is 
receding  from  the  sun  the  tail  goes  before  it,  as  has  been  said. 

(d)  Jets  and  Envelopes.  The  head  of  a  comet  is  often 
veined  by  short  jets  of  light,  which  appear  to  be  spurted 
out  from  the  nucleus ;  and  sometimes  the  nucleus  throws 
off  a  series  of  concentric  envelopes  like  hollow  shells,  one 
within  the  other.  These  phenomena,  however,  are  seldom 
observed  in  telescopic  comets. 

301.  Dimensions  of  Comets.  —  The  volume,  or  bulk,  of  a 
comet  is  often  enormous, — almost  inconceivably  so,  if  the 
tail  is  included  in  the  estimate.  The  head,  as  a  rule,  is 
from  40,000  to  50,000  miles  in  diameter  (comets  less  than 
10,000  miles  in  diameter  would  stand  little  chance  of  dis- 
covery). Comets  exceeding  150,000  miles  are  rather  rare, 
though  there  are  several  on  record. 

The  comet  of  1811  at  one  time  had  a  diameter  of  fully  1,200000 
miles,  —  forty  per  cent  larger  than  that  of  the  sun.  The  head  of  the 
comet  of  1680  was  600,000  miles  in  diameter,  and  that  of  Donati's 
comet  of  1858  about  250,000.  Holmes's  comet  (1892)  exceeded 
800,000. 

The  diameter  of  the  head  changes  continually  and 
capriciously ;  on  the  whole,  while  the  comet  is  approach- 
ing the  sun,  the  head  usually  contracts,  expanding  again 
as  it  recedes. 

No  entirely  satisfactory  explanation  is  known  for  this  behavior, 
but  Sir  John  Herschel  has  suggested  that  the  change  is  merely  optical, 
—  that  near  the  sun  a  part  of  the  nebulous  matter  is  evaporated 


MASS  OF  COMETS  263 

by  the  solar  heat  and  so  becomes  invisible,  condensing  and  reappear- 
ing again  when  the  comet  gets  to  cooler  regions. 

The  nucleus  ordinarily  has  a  diameter  ranging  from 
100  miles  up  to  5000  or  6000,  or  even  more.  Like  the 
comet's  head,  it  also  varies  greatly  in  diameter,  even  from 
day  to  day,  so  that  it  is  probably  not  a  solid  body.  Its 
changes,  however,  do  not  seem  to  depend  in  any  regular 
way  upon  the  comet's  distance  from  the  sun,  but  rather 
upon  its  activity  in  throwing  off  jets  and  envelopes. 

The  tail  of  a  comet,  as  regards  simple  magnitude,  is 
by  far  the  most  imposing  feature.  Its  length  is  sel- 
dom less  than  from  5,000000  to  10,000000  miles.  It 
frequently  attains  50,000000,  and  there  are  several  cases 
where  it  has  exceeded  100,000000;  while  its  diameter,  at 
the  end  remote  from  the  comet,  varies  from  1,000000 
to  15,000000. 

302.  Mass  of  Comets.  —  While  the  bulk  of  comets  is 
thus  enormous,  their  masses  are  apparently  insignificant,  — 
in  no  case  at  all  comparable  with  that  of  our  little  earth 
even.  The  evidence  on  this  point,  however,  is  purely  neg- 
ative ;  it  does  not  enable  us  in  any  case  to  say  just  what 
the  mass  really  is,  but  only  to  say  how  great  it  is  not: 
i.e.,  it  only  proves  that  a  comet's  mass  is  not  greater  than 
TTFTo  o"o  °^  the  earth's,1  —  how  much  less  we  cannot  yet 
find  out.  .  The  evidence  is  derived  from  the  fact  that  no 
sensible  perturbations  are  produced  in  the  motions  of  a 
planet  when  a  comet  comes  even  very  near  it,  although 
in  such  a  case  the  comet  itself  is  fairly  "sent  kiting," 

1  One  one-hundred-thousandth  of  the  earth's  mass  is  about  ten  times 
the  mass  of  the  earth's  whole  atmosphere  and  is  equivalent  to  the  mass 
of  an  iron  ball  about  150  miles  in  diameter. 


264  LESSONS  IN  ASTRONOMY 

thus  showing  that  gravitation  has  its  full  effect  between 
the  two  bodies. 

Lexell's  comet  in  1770,  and  Biela's  comet  on  several  occasions, 
have  come  so  near  the  earth  that  the  computed  length  of  the  comet's 
period  was  changed  by  several  weeks,  while  the  year  was  not  altered 
by  so  much  as  a  single  second.  It  would  have  been  changed  by 
many  seconds  if  the  comet's  mass  had  been  as  much  as  -nnforo  °f 
that  of  the  earth. 

303.  Density  of  Comets.  —  This  is,  of  course,  almost 
inconceivably  small,  the  mass  of  comets  being  so  minute 
and  their  volume  so  enormous.  If  the  head  of  a  comet 
50,000  miles  in  diameterxhas  a  mass  jo"oVo"o  that  °^  the 
earth,  its  mean  density  must  be  about  Q-^Q-Q  that  of  the  air 
at  the  sea-level,  —  far  below  that  of  the  best  air-pump 
vacuum.  As  for  the  tail,  the  density  must  be  almost 
infinitely  lower  yet.  It  is  nearer  to  an  "airy  nothing" 
than  anything  else  we  know  of. 

The  extremely  low  density  of  comets  is  shown  also  by 
their  transparency.  Small  stars  can  be  seen  through  the 
head  of  a  comet  100,000  miles  in  diameter,  even  very  near 
its  nucleus,  and  with  hardly  a  perceptible  diminution  of 
their  luster. 

We  must  bear  in  mind,  however,  that  the  low  mean  density  of  a 
comet  does  not  necessarily  imply  a  low  density  of  its  constituent 
particles.  A  comet  may  be  to  a  considerable  extent  composed  of 
small  heavy  bodies  and  still  have  a  low  mean  density,  provided  they 
are  far  enough  apart.  There  is  much  reason,  as  we  shall  see,  for 
supposing  that  such  is  really  the  case,  —  that  the  comet  is  largely 
composed  of  small  meteoric  stones,  carrying  with  them  a  certain 
quantity  of  enveloping  gas. 

Another  point  should  be  referred  to.  Students  often 
find  it  impossible  to  conceive  how  such  impalpable  "dust 


THE  LIGHT  OF  COMETS  265 

clouds"  can  move  in  orbits  like  solid  masses,  and  Avith 
such  enormous  velocities.  They  forget  that  in  a  vacuum 
a  feather  falls  as  swiftly  as  a  stone.  Interplanetary  space 
is  a  vacuum  far  more  perfect  than  anything  we  can  pro- 
duce by  air-pumps,  and  in  it  the  lightest  bodies  move  as 
freely  and  swiftly  as  the  densest,  since  there  is  nothing  to 
resist  their  motion.  If  all  the  earth  were  suddenly  anni- 
hilated except  a  single  feather,  the  feather  would  keep  right 
on  and  continue  the  same  orbit  with  unchanged  speed. 

304.  The  Light  of  Comets.  —  To  some  extent  their  light 
may  be  mere  reflected  sunlight,  \p*k  in  the  main  it  is  light 
emitted  by  the  comet  itself  under  the  stimulus  of  solar 
action.  That  the  light  depends  in  some  way  on  the  sun 
is  shown  by  the  fact  that  its  brightness  usually  varies  with 
its  distance  from  the  sun,  according  to  the  same  law  as 
that  of  a  planet. 

But  the  brightness  frequently  varies  rapidly  and  capri- 
ciously without  any  apparent  reason ;  and  that  the  comet 
is  self-luminous  when  near  the  sun  is  proved  by  its  spectrum, 
which  is  not  at  all  like  the  spectrum  of  reflected  sunlight, 
but  is  a  spectrum  of  bright  bands,  three  of  which  are  usually 
seen  and  have  been  identified  repeatedly  and  certainly  with 
the  spectrum  of  gaseous  hydrocarbons.  (All  the  different 
hydrocarbon  gases  give  the  same  spectrum  at  the  tempera- 
ture of  a  Bunsen  burner.)  This  spectrum  is  absolutely  iden- 
tical with  that  given  by  the  blue  base  of  a  candle  flame,  or, 
better,  by  a  Bunsen  burner  consuming  ordinary  coal  gas. 

Occasionally  a  fourth  band  is  seen  in  the  violet,  and  when  the  comet 
approaches  unusually  near  the  sun,  the  bright  lines  of  sodium  and 
other  metals  (probably  iron),  sometimes  appear.  There  are  also  a  few 
comets  with  anomalous  spectra  in  which  different  bands  replace  the 


266 


LESSONS  IN  ASTRONOMY 


ordinary  ones,  as  in  the  case  of  Borrelly's  comet  of  1877.  Holmes's 
comet  in  1892  showed  a  purely  continuous  spectrum.  The  spectrum 
makes  it  almost  certain  that  hydrocarbon  gases  are  present  in  con- 
siderable quantity,  and  that  these  gases  are  somehow  rendered  lumi- 
nous ;  not  probably  by  any  general  heating,  however,  for  there  is  no 


FIG.  69.  —Head  of  Donati's  Comet 
Bond 

reason  to  think  that  the  general  temperature  of  a  comet  is  very  high. 
Nor  must  we  infer  that  the  hydrocarbon  gas,  because  it  is  so  con- 
spicuous in  the  spectrum,  necessarily  constitutes  most  of  the  comet's 
mass ;  more  likely  it  is  only  a  very  small  fraction  of  the  whole. 


COMETARY  PHENOMENA 


267 


To  Sun 


305.  Phenomena  that  accompany  a  Comet's  Approach  to 
the  Sun.  —  When  the  comet  is  first  discovered  it  is  usually 
a  mere  round,  hazy  cloud  of  faint  nebulosity,  a  little  brighter 
near  the  middle.     As  it  approaches  the  sun  it  brightens 
rapidly,  and  the  nucleus  appears.     Then  on  the  sunward 
side  the  nucleus  begins  to  emit  luminous  jets,  or  else  to 
throw  off  more  or  less  symmetrical  envelopes,  which  follow 
each  other  at  intervals  of 

some  hours,  expanding  or 
growing  fainter,  until  they 
are  lost  in  the  nebulosity  of 
the  head. 

Fig.  69  shows  the  envel- 
opes as  they  appeared  in 
the  head  of  Donati's  comet 
of  1858.  At  one  time 
seven  of  them  were  visible 
together  ;  very  few  comets, 
however,  exhibit  this  phe- 
nomenon with  such  sym- 
metry. More  frequently 
the  emissions  from  the  nucleus  take  the  form  of  jets 
and  streamers. 

306.  Formation  of  Tail.  —  The  tail  appears  to  be  formed 
of  material  which  is  first  projected  from  the  nucleus  of 
the  comet  towards  the  sun  and  then  afterwards  repelled 
by  the  sun,  as  illustrated  by  Fig.  70.     At  least,  this  theory- 
has  the  great  advantage  over  all  others  which  have  been 
proposed  that  it  not  only  accounts  for  the  phenomenon 
in  a  general  way,  but  admits  of  being  worked  out  in  detail 
and  verified  mathematically,  by  comparing  the  actual  size 


FIG.  70.  —  Formation  of  a  Comet's  Tail 
by  Matter  expelled  from  the  Head 


268  LESSONS  IN  ASTRONOMT 

and  form  of  the  comet's  tail  at  different  points  in  the  orbit 
with  that  indicated  by  the  theory  ;  and  the  accordance  is 
usually  satisfactory. 

As  to  the  nature  of  this  repulsive  force  there  has  been  much  specu- 
lation. For  some  time  it  has  generally  been  believed  to  be  electrical, 
and  it  is  still  probable  that  such  forces  play  an  important  part.  But 
the  recent  experimental  demonstrations  (1901-1902)  of  the  repul- 
sive force  of  light-waves,  long  ago  pointed  out  by  Clerk  Maxwell 
as  a  necessary  consequence  of  his  electro-magnetic  theory  of  light 
(now  regarded  as  established . by  the  experiments  of  Herz),  make  it 
almost  certain  that  this  is  the  principal  agent  in  driving  off  the  come- 
tary  particles.  The  two  theories  are,  however,  supplementary  rather 
than  contradictory. 

The  repelled  particles  are  still  subject  to  the  sun's  gravi- 
tational attraction,  and  the  effective  force  acting  upon  them 
is,  therefore,  the  difference  between  the  gravitational  attrac- 
tion and  the  repulsion.  This  difference  may  or  may  not 
be  in  favor  of  the  attraction,  but  in  any  case  the  sun's 
attracting  force  is,  at  least,  lessened.  The  consequence  is 
that  those  repelled  particles,  as  soon  as  they  get  a  little 
away  from  the  comet,  begin  to  move  around  the  sun  in 
hyperbolic  orbits  (see  Sec.  439),  which  lie  in  the  plane  of 
the  comet's  orbit,  or  nearly  so,  and  are  perfectly  amenable 
to  calculation. 

In  the  case  of  a  great  comet  the  tail  is  usually  a  sort  of 
curved,  hollow  cone,  including  the  head  of  the  comet  at 
its  smaller  extremity ;  in  smaller  comets  the  tail  is  gener- 
ally a  comparatively  narrow  streamer  where  it  issues  from 
the  head  of  the  comet,  brushing  out  as  it  recedes,  and  often 
showing  in  photographs  peculiar  knots  and  condensations, 
which  are  not  visible  with  the  telescope. 


FORMATION  OF  COMETS'  TAILS  269 

The  tail  is  curved,  because  the  repelled  particles,  after 
leaving  the  comet's  head,  retain  their  original  motion,  so 
that  they  are  arranged,  not  along  a  straight  line  drawn 
from  the  sun  to  the  comet,  but  on  a  curve  convex  to  the 
comet's  motion,  as  shown  in  Fig.  71 ;  but  the  stronger 
the  repulsion,  the  less  the  curvature  and  the  straighter  the 
tail.  There  is  no  reason  to  suppose  that  the  matter  driven 
off  from  the  comet  is  ever  recovered  by  it. 


FIG.  71.  —  A  Comet's  Tail  at  Different  Points  in  its  Orbit  near  Perihelion 

307.  Types  of  Comets'  Tails.  —  Bredichin  of  Moscow 
has  found  that  the  trains  of  comets  may  be  classified  under 
three  different  types,  as  indicated  by  Fig.  72. 

First.  The  long,  straight  rays,  composed  of  matter  upon  which  the 
solar  repulsion  is  from  ten  to  fifteen  times  as  great  as  the  attraction 
of  gravity,  so  that  the  particles  leave  the  comet  with  a  velocity  of 
four  or  five  miles  a  second,  which  is  afterwards  increased  until  it 
becomes  enormous.  The  nearly  straight  rays,  shown  in  Fig.  67, 
belong  to  this  type.  For  plausible  reasons,  Bredichin  supposes  these 
straight  rays  to  be  composed  of  hydrogen. 


270 


LESSONS  IN  ASTRONOMY 


The  second  type  is  the  ordinary  curved   plumelike   train,   like 
the  principal  tail  of  Donati's  comet.     In  trains  of  this  type,  supposed 

to  be  due  to  hydrocarbon 
vapors,  the  repulsive  force 
varies  from  2.2  times  the 
attraction  of  gravity  for 
particles  on  the  convex 
edge  of  the  train  to  half 
that  amount  for  those  on 
the  inner  edge.  The  spec- 
trum is  the  same  as  that 
of  the  comet's  head. 

Third.  A  few  comets 
show  tails  of  still  a  third 
type,  —  short,  stubby 
brushes,  violently  curved, 
and  due  to  matter  on 
which  the  repulsive  force 
is  feeble  as  compared 
with  gravity.  These  are 
assigned  by  Bredichin  to 
metallic  vapors  of  consid- 
erable density,  with  an  ad- 
mixture of  sodium,  etc. 

308.  Unexplained 
and  Anomalous  Phe- 
nomena. —  A  curious 
phenomenon,  not  yet 
explained,  is  the  dark 
stripe  which  in  a  large 

FIG.  72.  —  Bredichin 's  Three  Types  of  comet  approaching  the 

Cometary  Tails  ,  , 

sun  runs  down  the 

center  of  the  tail,   looking  very   much   as  if  it  were  a 
shadow  of  the  comet's  head.     It  is  certainly  not  a  shadow, 


NATURE   OF  COMETS  271 

however,  because  it  usually  makes  more  or  less  of  an  angle 
with  the  sun's  direction.  It  is  well  shown  in  Fig.  69. 
When  the  comet  is  at  a  greater  distance  from  the  sun 
this  central  stripe  is  usually  bright,  as  in  Fig.  73  ;  and 
in  the  case  of  small  comets,  generally  all  the  tail  they 
show  is  such  a  narrow  streamer. 

Not  unfrequently,  moreover,  comets  possess  anomalous  tails, — 
tails  directed  sometimes  straight  towards  the  sun  and  sometimes 
at  right  angles  to  that  direction. 
Then  sometimes  there  are  luminous 
sheaths,  which  seem  to  envelop  the 
head  of  the  comet  and  project 
towards  the  sun  (Fig.  74),  or  little 
clouds  of  cometary  matter,  which 
leave  the  main  comet,  like  puffs  of 
smoke  from  a  bursting  bomb,  and  ^73.  -  Bright-Centered  Tail  of 

Coggia's  Comet,  June,  1874 
travel   off   at   an  angle  until   they 

fade  away  (see  Fig.  74).  None  of  these  appearances  are  contradic- 
tory to  the  theory  above  stated  though  they  are  not  yet  clearly 
included  in  it. 

309.  The  Nature  of  Comets.  —  All  things  considered, 
the  most  probable  hypothesis  as  to  the  constitution  of  a 
comet,  so  far  as  we  can  judge  at  present,  is  that  its  head 
is  a  swarm  of  small  meteoric  particles,  widely  separated 
(say  pinheads,  many  yards  apart),  each  carrying  with  it 
an  envelope  of  rarefied  gas  and  vapor,  in  which  light 
is  produced  either  by  electric  discharges  between  the 
solid  particles,  or  by  some  action  due  to  the  rays  of  the 
sun.  As  to  the  size  of  the  constituent  particles  opinions 
differ  widely.  Some  maintain  that  they  are  large  rocks ; 
Professor  Newton  calls  a  comet  a  "  gravel  bank  " ;  others 
say  that  it  is  a  mere  "  dust  cloud."  The  unquestionable 


272  LESSONS  IN  ASTRONOMY 

close  connection  between  meteors  and  comets  (Sec.  327) 
almost  compels  some  "  meteoric  hypothesis." 

310.  Danger  from  Comets.  —  In  all  probability  there  is  very 
little.  It  has  been  supposed  that  comets  might  do  us  harm  in  three 
ways,  —  either  by  actually  striking  the  earth  or  by  falling  into  the 
sun,  and  thus  producing  such  an  increase  of  solar  heat  as  to  burn  us 
up,  or,  finally,  by  filling  our  atmosphere  with  irrespirable  if  not 
poisonous  gases. 

As  regards  the  possibility  of  a  collision  between  a  comet  and  the 
earth,  the  event  is  certainly  possible.  In  fact,  if  the  earth  lasts  long 
enough,  it  is  practically  sure  to  happen,  for  there  are  several  cometary 
orbits  which  pass  nearer  to  the  earth's  orbit  than  the  semi-diameter 
of  the  comet's  head. 

As  to  the  consequence  of  such  a  collision,  it  is  impossible  to  speak 
with  absolute  confidence  for  want  of  certain  knowledge  as  to  the 
constitution  of  a  comet.  If  the  solid  "  particles  "  of  which  the  main 
portion  of  the  comet  is  probably  composed  are  no  larger  than  pin- 
heads,  the  result  would  be  only  a  fine  meteoric  shower ;  if,  on  the 
other  hand,  they  weigh  tons,  the  bombardment  would  be  a  very 
serious  matter.  It  is  possible  too  that  the  mixture  of  the  comet's 
gases  with  our  atmosphere  might  be  a  source  of  danger  by  rendering 
the  air  irrespirable  or  explosive. 

The  encounters,  however,  will  be  very  rare.  If  we  accept  the 
estimate  of  Babinet,  they  will  occur  on  the  average  once  in  about 
15,000000  years. 

If  a  comet  actually  strikes  the  sun,  which  would  necessarily  be  a 
very  rare  phenomenon,  it  is  not  likely  that  the  least  injury  will  fol- 
low. The  collision  might  generate  about  as  much  heat  as  the  sun 
radiates  in  eight  or  nine  hours  ;  but  the  cometary  particles  would 
pierce  the  photosphere,  and  their  heat  would  be  liberated  mostly 
below  the  solar  surface,  simply  expanding  by  some  slight  amount 
the  diameter  of  the  sun,  but  making  no  particular  difference  in  the 
amount  of  its  radiation  for  the  time  being.  There  might  be,  and 
very  likely  would  be,  a  flash  of  some  kind  at  the  solar  surface  when 
the  shower  of  meteors'  struck  it,  but  probably  nothing  that  the 
astronomer  would  not  take  delight  in  observing. 


REMARKABLE  COMETS  273 

311.  Remarkable  Comets.  —  Our  space  does  not  permit 
us  to  give  full  accounts  of  any  considerable  number.     We 
limit  ourselves  to  three,  which  for  various  reasons  are  of 
special  interest. 

Biela's  comet  is,  or  rather  was,  a  small  comet  some  40,000 
miles  in  diameter,  at  times  barely  visible  to  the  naked  eye, 
and  sometimes  showing  a  short  tail.  It  had  a  period  of 
6.6  years,  and  was  the  second  comet  of  short  period 
known,  having  been  discovered  by  Biela,  an  Austrian 
officer,  in  1826  (the  periodicity  of  Encke's  comet  had 
been  discovered  seven  years  earlier).  Its  orbit  comes 
within  a  few  thousand  miles  of  the  earth's  orbit,  the  dis- 
tance varying  somewhat,  of  course,  on  account  of  per- 
turbations; but  the  approach  is  ^sometimes  so  close  that 
if  the  comet  and  the  earth  should  happen  to  arrive  at 
the  same  time  there  would  be  a  collision.  At  its  return, 
in  1846,  it  split  into  two.  When  first  seen  on  Novem- 
ber 28,  it  was  one  and  single.  On  December  19  it  was 
distinctly  pear-shaped,  and  ten  days  later  it  was  divided. 

The  twin  comets  traveled  along  for  four  months  at  an  almost 
unchanging  distance  of  about  165,000  miles,  without  any  apparent 
effect  upon  each  other's  motions,  but  both  very  active  from  the  physical 
point  of  view,  and  showing  remarkable  variations  and  alternations  of 
brightness  entirely  unexplained.  In  August,  1852,  the  twins  were 
again  observed,  then  separated  by  a  distance  of  about  1,500000 
miles ;  but  it  was  impossible  to  tell  which  was  which.  Neither  of 
them  has  ever  been  seen  again,  though  they  must  have  returned 
many  times,  and  more  than  once  in  a  very  favorable  position. 

312.  There  remains,  however,  another  remarkable  chap- 
ter in  the  story  of  this  comet.     In  1872,  on  November  27, 
just  as  the  earth  was  crossing  the  track  of  the  lost  comet, 


274  LESSONS  IN  ASTRONOMY 

but  some  millions  of  miles  behind  where  the  comet  ought 
to  be,  we  encountered  a  wonderful  meteoric  shower.  As 
Miss  Clerke  expresses  it,  perhaps  a  little  too  positively, 
"  it  became  evident  that  Biela's  comet  was  shedding  over 
us  the  pulverized  products  of  its  disintegration."  A  similar 
meteoric  shower  occurred  again  in  1885  (see  also  Sec.  326), 
when  the  earth  once  more  crossed  the  track  of  the  comet ; 
and  still  again  in  1892  and  1898,  —  the  last  very  feeble. 

It  is  not  certain  whether  the  meteor  swarms  thus  encountered 
were  the  remains  of  the  comet  itself,  or  whether  they  were  other  small 
bodies  merely  following  in  its  path.  The  comet  must  have  been  several 
millions  of  miles  ahead  of  the  place  where  these  meteor  swarms  were 
met,  unless  it  has  been  set  back  in  its  orbit  since  1852  by  some  unex- 
plained and  improbable  perturbations.  But  the  comet  cannot  be 
found,  and  if  it  still  exists  and  occupies  the  place  it  ought  to,  it  must 
have  somehow  lost  the  power  of  shining. 

313.  The  Great  Comet  of  1882.  —  This  is  the  most  recent 
of  the  brilliant  comets  observed  in  the  United  States,  and 
will  long  be  remembered  not  only  for  its  magnificent  beauty, 
but  for  the  great  number  of  unusual  phenomena  which  it 
presented.  It  was  first  seen  in  the  southern  hemisphere 
about  September  3,  but  not  in  the  northern  until  the  17th, 
the  day  on  which  it  arrived  at  perihelion.  On  that  day  it 
was  independently  discovered  within  2°  or  3°  of  the  sun,  near 
noon,  by  several  observers,  who  had  not  before  heard  of  its 
existence.  It  was  visible  to  the  naked  eye  in  full  sunshine 
for  more  than  a  week  after  its  perihelion  passage.  It  then 
became  a  splendid  object  in  the  morning  sky  and  continued 
to  be  observed  for  six  months. 

That  portion  of  the  orbit  visible  from  the  earth  coincides 
almost  exactly  with  the  orbits  of  four  other  comets,  —  those 


THE   GREAT   COMET  OF   1882  275 

of  1668,  1843,  1880,  and  1887,  with  which  it  forms  a 
"comet-group,"  as  already  mentioned  (Sec.  294).  The 
perihelion  distances  of  the  comets  of  this  group  are  all 
less  than  750,000  miles,  so  that  they  pass  within  300,000 
miles  of  the  sun's  surface,  i.e.,  right  through  the  corona, 
and  with  a  velocity  exceeding  300  miles  a  second;  and 
yet  this  passage  through  the  corona  does  not  perceptibly 
disturb  their  motion. 

The  orbit  of  the  comet  of  1882  turned  out  to  be  a  very 
elongated  ellipse  with  a  period  of  about  800  years.  The 
periods  of  the  others  are  quite  uncertain  because  they 
could  not  be  observed  as  long,  but  the  orbits  of  all  are 
probably  similar  in  every  respect. 

Early  in  October  the  comet  presented  the  ordinary 
features.  The  nucleus  was  round,  a  number  of  well- 
marked  envelopes  were  visible  in  the  head,  and  the  dark 
stripe  down  the  center  of  the  tail  was  sharply  defined. 
Two  weeks  later  the  nucleus  had  been  broken  up  and 
transformed  into  a  crooked  stream  some  50,000  miles  in 
length,  of  five  or  six  bright  points;  the  envelopes  had 
vanished  from  the  head,  and  the  dark  stripe  was  replaced 
by  a  bright  central  spine. 

At  the  time  of  perihelion  the  comet's  spectrum  was 
filled  with  countless  bright  lines.  Those  of  sodium  were 
easily  recognizable,  and  continued  visible  for  weeks;  the 
other  lines  continued  only  a  few  days  and  were  not 
certainly  identified,  although  the  general  aspect  of  the 
spectrum  indicated  that  iron,  manganese,  and  calcium 
were  probably  present.  By  the  middle  of  October  it 
had  become  simply  the  normal  comet  spectrum  with  the 
ordinary  hydrocarbon  bands. 


276  LESSONS  IN  ASTROXOMY 

The  comet  was  so  situated  that  the  tail  was  directed 
nearly  away  from  the  earth,  and  so  was  not  seen  to  good 
advantage,  never  having  an  apparent  length  exceeding  35°. 
The  actual  length,  however,  at  one  time  was  more  than 
100,000000  miles. 

A  unique,  and  still  only  doubtfully  explained,  phenom- 
enon, was  a  faint,  straight-edged  "  sheath  "  of  light,  which 


FIG.  74.  — The  "  Sheath,"  and  the  Attendants  of  the  Comet  of  1882 

enveloped  the  portions  of  the  comet  near  the  head  and 
projected  3°  or  4°  in  front  of  it,  as  shown  in  Fig.  74. 
Moreover,  there  were  certain  shreds  of  cometary  matter 
accompanying  the  comet, at  a  distance  of  3°  or  4°  when 
first  seen,  but  gradually  receding  and  growing  fainter. 


PHOTOGRAPHY  OF  COMETS  277 

This  also  was  something  new  in  cometary  history,  though 
the  Lexell-B rooks  comet,  1889— V,  has  since  shown  some- 
thing much  like  it. 

314.  Halley's  Comet.  —  The  most  brilliant  of  the  peri- 
odic comets  is  Halley's,  which  was  seen  last  in  1910  and  is 
due  to  appear  again  about  1985.  This  is  undoubtedly  the 
same  comet  that  was  seen  in  1066,  the  year  of  the  Norman 
Conquest,  and  was  probably  seen  as  early  as  11  B.C. 

Its  path  is  very  oval,  extending  beyond  the  orbit  of  the 
planet  Neptune.  It  reappears  every  75  or  76  years,  and 
when  near  perihelion  is  usually  a  conspicuous  object.  On 
May  18,  1910,  it  passed  between  the  earth  and  the  sun, 
coming  so  near  to  us  that  the  earth  must  have  passed 
through  at  least  a  part  of  its  tail,  but  not  the  slightest 
effect  on  the  earth  could  be  detected,  nor  could  any  trace 
of  the  comet  be  seen  when  passing  across  the  sun's  face. 

314*.  Photography  of  Comets.  —  It  is  now  possible  to 
photograph  comets,  and  the  photographs  bring  out  numer- 
ous peculiarities  and  details,  which  are  not  visible  to  the 
eye  even  with  telescopic  aid.  This  is  especially  the  case 
in  the  comet's  tail.  The  figure  on  the  next  page  is  from 
a  magnificent  photograph  of  Rordame's  comet  of  1893, 
for  which  we  are  indebted  to  the  kindness  of  Professor 
Holden,  director  of  the  Lick  Observatory.  As  the  camera 
was  kept  pointed  at  the  head  of  the  comet  (which  was  mov- 
ing pretty  rapidly),  the  star  images,  during  the  hour's 
exposure,  are  drawn  out  into  parallel  streaks,  the  little 
irregularities  being  due  to  faults  of  the  clockwork  and 
vibrations  of  the  telescope.  The  knots  and  streamers, 
which  characterize  the  comet's  tail,  were  none  of  them 
visible  in  the  telescope  and  are  not  the  same  shown  upon 


FIG.  75.  —Comet  Rordame,  July  13,  1893 
Photographed  by  W.  J.  Hussey,  at  the  Lick  Observatory 

278 


PHOTOGRAPHY  OF  COMETS 


279 


plates  taken  the  day  before  and  the  day  after.  Other 
plates,  made  the  same  evening  a  few  hours  earlier  and 
later,  indicate  that  the  "knots"  were  swiftly  receding 
from  the  comet's  head  at  a  rate  exceeding  150,000 
miles  an  hour.  It  is  to  be  noted  also  that  the  light 
of  a  comet's 
tail  seems  to 
be  specially 
"actinic,"  so 
that,  as  in  the 
case  of  the 
nebulae,  photo- 
graphs show 
features  and 
details  which 
are  entirely 
invisible  in 
telescopes. 

Fig.  76  shows  Swift's  comet  of  1892,  at  three  different 
dates  as  photographed  by  Barnard  at  the  Lick  Observa- 
tory. The  rapid  changes  in  the  structure  of  the  tail  'are 
very  remarkable  and  significant. 

In  1892  Barnard  discovered  a  small  comet  by  the  streak,  it  left 
upon  one  of  his  star  plates,  and  several  similar  discoveries  have  since 
been  made  by  others. 


FIG.  76.  —  Swift's  Comet  of  1892 
Photographed  by  Barnard 


METEORS   AND   SHOOTINO-STARS 

315.  Meteorites.  —  Occasionally  bodies  fall  upon  the 
earth  out  of  the  sky.  Such  a  body  during  its  flight 
through  the  air  is  called  a  "  Meteor  "  or  "  Bolide,"  and  the 


280  LESSONS  IN  ASTRONOMY 

pieces  which  fall  to  the  earth  are  called  "  Meteorites," 
44  Aerolites,"  "  Uranolites,"  or  simply  "  meteoric  stones." 
If  the  fall  occurs  at  night,  a  ball  of  fire  is  seen,  which 
moves  with  an  apparent  velocity  depending  upon  the  dis- 
tance of  the  meteor  and  the  direction  of  its  motion.  The 
fire-ball  is  generally  followed  by  a  luminous  train,  which 
sometimes  remains  visible  for  many  minutes  after  the  meteor 
itself  has  disappeared.  The  motion  is  usually  somewhat 
irregular,  and  here  and  there  along  its  path  the  meteor 
throws  off  sparks  and  fragments  and  changes  its  course 
more  or  less  abruptly.  Sometimes  it  vanishes  by  simply 
fading  out  in  the  air,  sometimes  by  bursting  like  a  rocket. 
If  the  observer  is  near  enough,  the  flight  is  accompanied 
by  a  heavy  continuous  roar,  emphasized  now  and  then  by 
violent  detonations. 

The  observer  must  not  expect  to  hear  the  explosion  at  the  moment 
when  he  sees  it,  since  sound  travels  only  about  twelve  miles  a  minute. 

If  the  fall  occurs  by  day,  the  luminous  appearances  are 
mainly  wanting,  though  sometimes  a  white  cloud  is  seen, 
and  the  train  may  be  visible.  In  a  few  cases  a°erolites 
have  fallen  almost  silently,  and  without  warning. 

316.  The  Aerolites  themselves.  —  The  mass  that  falls  is 
sometimes  a  single  piece,  but  more  usually  there  are  many 
fragments,  sometimes  numbering  thousands;  so  that,  as 
the  old  writers  say,  "  it  rains  stones."  The  pieces  observed 
to  fall  weigh  from  six  hundred  pounds  to  a  few  grains, 
the  aggregate  mass  sometimes  amounting  to  a  number  of 
tons.  By  far  the  greater  number  of  aerolites  are  stones,  but 
a  few  —  perhaps  three  or  four  per  cent  of  the  whole  num 
ber  —  are  masses  of  nearly  pure  iron  more  or  less  alloyed 


THE  AEROLITES  THEMSELVES  281 

with  nickel.  There  are  also  masses  of  so-called  "  meteoric 
iron  "  which  have  been  found  (not  seen  to  fall)  in  places 
where  it  is  not  easy  otherwise  to  account  for  their  pres- 
ence, and  one  of  these  (Peary's,  from  Greenland)  weighs 
nearly  seventy  tons.  But  their  meteoric  character  is  con- 
sidered extremely  doubtful  by  the  highest  authorities. 

The  total  number  of  meteorites  which  have  fallen  and  been  gath- 
ered into  cabinets  since  1800  is  about  275,  —  only  10  of  which  are 
iron  masses.  Nearly  all,  however,  contain  a  large  percentage  of  iron, 
either  in  the  metallic  form  or  as  sulphide.  Between  25  and  30  of 
the  250  fell  within  the  United  States,  the  most  remarkable  being 
those  of  Weston,  Conn.,  in  1807;  New  Concord,  Ohio,  I860; 
Amana,  Iowa,  1875;  Emmet  County,  Iowa,  1879  (mainly  iron); 
and  Johnson  County,  Ark.,  1886  (iron). 

Twenty-five  of  the  chemical  elements  have  been  found 
in  these  bodies,  including  helium  (Sec.  181),  but  not  one 
new  element ;  though  a  large  number  of  new  minerals  (i.e., 
new  compounds  of  known  elements)  appear  in  them,  and 
seem  to  be  characteristic  of  aerolites. 

The  most  distinctive  external  feature  of  a  meteorite  is 
the  thin,  black,  varnishlike  crust  that  covers  it.  It  is 
formed  by  the  melting  of  the  surface  during  the  meteor's 
swift  flight  through  the  air,  and  in  some  cases  penetrates 
the  mass  in  cracks  and  veins.  The  surface  is  generally 
somewhat  uneven,  having  "  thumb-marks "  upon  it,  — 
hollows,  probably  formed  by  the  fusion  of  some  of  the 
softer  minerals.  Fig.  77  is  from  a  photograph  of  a  mete- 
orite weighing  twenty-four  pounds,  which  fell  in  Hungary 
in  1837,  —  one  of  several  which  fell  together. 

317.  Path  and  Motion.  —  When  a  meteor  has  been  well 
observed  from  a  number  of  different  stations,  its  path  can 


282  LESSONS  IN  ASTRONOMY 

be  computed.  Tt  usually  is  first  seen  at  an  altitude  of 
between  80  and  100  miles  and  disappears  at  an  altitude  of 
between  5  and  10.  The  length  of  the  path  may  be  any- 
where from  50  to  500  miles.  In  the  earlier  part  of  its 
course  the  velocity  ranges  from  10  to  40  miles  a  second, 
but  this  is  greatly  reduced  before  the  meteor  disappears. 

In  observing  these  bodies,  the  object  should  be  to  obtain  as  accu- 
rate an  estimate  as  possible  of  the  altitude  and  azimuth  of  the  meteor 


FIG.  77.  — The  Gross  Divina  Meteorite 

at  moments  which  can  be  identified,  and  also  of  the  time  occupied  in 
traversing  definite  portions  of  the  path.  The  altitude  and  azimuth 
will  enable  us  to  determine  the  height  and  position  of  the  meteor, 
while  the  observations  of  the  time  are  necessary  in  computing  its 
velocity.  By  night  the  stars  furnish  the  best  reference  points  from 
which  to  determine  its  position.  By  day  one  must  take  advantage 
of  natural  objects  or  buildings  to  define  the  meteor's  place,  the 
observer  marking  the  precise  spot  where  he  stood.  By  taking  the 
proper  instrument  to  the  place  afterwards  it  is  then  easy  to  ascer- 
tain the  bearings  and  altitude.  As  to  the  time  of  flight,  it  is  usual 


LIGHT  AND  HEAT  OF  METEORS  283 

for  the  observer  to  begin  to  repeat  rapidly  some  familiar  verse  of 
doggerel  when  the  meteor  is  first  seen,  reiterating  it  until  the  meteor 
disappears.  Then,  by  rehearsing  the  same  before  a  clock,  the 
number  of  seconds  can  be  pretty  accurately  determined. 

318.  The  Light  and  Heat  of  Meteors.  —  These  are  due 
simply  to  the  destruction  of  the  meteor's  velocity  by  the 
friction,  compression,  and  resistance  of  the  air.     When  a 
body  moving  with  a  high  velocity  is  stopped  by  the  resist- 
ance of  the  air,  the  greater  part  of  its  energy  is  trans- 
formed into  heat.     Lord  Kelvin  has  demonstrated  that  the 
heating  effect  in  the  case  of  a  body  moving  through  the 
air   with   a   velocity   exceeding   ten    miles    a    second    is 
the  same  as  if  it  were  "  immersed  in  a  flame  having  a  tem- 
perature at  least  as  high  as  the  oxyhydrogen  blowpipe  "  ; 
and,  moreover,   this    temperature   is   independent   of  the 
density  of  the  air,  —  depending  only  on  the  velocity  of  the 
meteor.     Where  the    air  is    dense,  the  total  quantity  of 
heat  (i.e.,  the  number  of  calories  developed  in  a  given  time) 
is,  of  course,  greater  than  where  the  air  is  rarefied ;  but  the 
virtual  temperature  of  the  air  itself  where  it  rubs  against 
the    surface   is    the    same    in    either   case.      During   the 
meteor's  flight,  its  surface,  therefore,  is  raised  to  a  white 
heat  and  melted,  and  the  liquefied  portions  are  swept  off 
by  the  rush  of  air,  condensing  as   they  cool  to  form  the 
train.     In  some  cases  this  train  remains  visible  for  many 
minutes,  —  a  fact  not  easily  explained.     It  seems  probable 
that  the  material  must  be  phosphorescent. 

319.  Origin  of  Meteors.  —  They  cannot  be,  as  some  have 
maintained,  the  immediate  product  of  eruptions  from  vol- 
canoes, either  terrestrial  or  lunar,  since  they  reach  our 
atmosphere  with  a  velocity  which  makes  it  certain  that 


284  LESSONS  IN  ASTRONOMY 

they  come  to  us  from  the  depths  of  space.  There  is  no 
proof  that  they  have  originated  in  any  way  different  from 
the  larger  heavenly  bodies.  At  the  same  time  many  of 
them  resemble  each  other  so  closely  as  almost  to  compel 
the  surmise  that  these,  at  least,  must  have  had  a  common 
source.  It  is  not  perhaps  impossible  that  such  may  be 
fragments  which  long  ago  were  shot  out  from  now  extinct 
lunar  volcanoes  with  a  velocity  which  made  planets  of 
them  for  the  time  being.  If  so,  they  have  since  been 
traveling  in  independent  orbits  until  they  encountered 
the  earth  at  the  point  where  her  orbit  crosses  theirs.  Nor 
is  it  impossible  that  some  of  them  were  thrown  out  by 
terrestrial  eruptions  when  the  earth  was  young,  or  that 
they  have  been  ejected  from  other  planets,  or  even  from 
the  stars.  It  is  only  certain  that  during  the  period 
immediately  preceding  their  arrival  upon  the  earth  they 
have  been  traveling  in  long  ellipses  or  parabolas,  around 
the  sun. 

SHOOTING-STARS 

320.  Their  Nature  and  Appearance.  —  These  are  the 
evanescent,  swiftly  moving,  starlike  points  of  light  which 
may  be  seen  every  few  minutes  on  any  clear  moonless 
night.  They  make  no  sound,  nor  has  anything  been 
certainly  known  to  reach  the  earth's  surface  from  them. 

For  this  reason  it  is  probably  best  to  retain,  provisionally,  at 
least,  the  old  distinction  between  them  and  the  great  meteors  from 
which  aerolites  fall.  It  is  quite  possible  that  the  distinction  has  no 
real  ground,  that  shooting-stars,  as  is  maintained  by  many,  are 
just  like  other  meteors,  except  that  being  so  small  they  are  entirely 
consumed  in  the  air  ;  but  then,  on  the  other  hand,  there  are  some 
things  which  rather  favor  the  idea  that  the  two  classes  differ  in 


SHOOTING-STARS  285 

about  the  same  way  as  asteroids  do  from  comets.  We  know  that  an 
aerolitic  meteor  is  a  compact  mass  of  rock.  It  is  possible,  and  not 
even  unlikely,  that  a  shooting-star,  on  the  contrary,  is  a  little  dust 
cloud,  —  like  a  puff  of  smoke. 

321.  Number  of  Shooting-Stars.  — Their  number  is  enor- 
mous.    A  single  observer  averages  from  four  to  eight  an 
hour;  but  if  the  observers  are  sufficiently  numerous  and 
so  placed  as  to  be  sure  of  noting  all  that  are  visible  from 
a  given  station,  about  eight  times  as  many  are  counted. 
From  this  it  has  been  estimated  that  the  total  number 
which   enter   our    atmosphere    daily    must    be    between 
10,000000  and  20,000000,  the  average  distance  between 
them  being  some  200  miles. 

Besides  those  which  are  visible  to  the  naked  eye,  there  is  a  still 
larger  number  of  meteors  which  are  so  small  as  to  be  observable 
only  with  the  telescope. 

The  average  hourly  number  about  six  o'clock  in  the 
morning  is  double  the  hourly  number  in  the  evening, 
the  reason  being  that  in  the  morning  we  are  in  front 
of  the  earth  as  regards  its  orbital  motion,  while  in  the 
evening  we  are  in  the  rear.  In  the  evening  we  see  only 
such  as  overtake  us ;  in  the  morning  we  see  all  that  we 
either  meet  or  overtake. 

322.  Elevation,  Path,  and  Velocity.  —  By  observations 
made  at  stations  30  or  40  miles  apart  it  is  easy  to  deter- 
mine these  data  with  some  accuracy.     It  is  found  that  on 
the  average  the  shooting-stars  appear  at  a  height  of  about 
74  miles  and  disappear  at  an  elevation  of  about  50  miles, 
after  traversing  a  course  40  or  50  miles  long,  with  a  velocity 
from  10  to  50  miles  a  second,  —  about  25  on  the  average. 
They  do  not  first  become  visible  at  so  great  a  height  as 


286  LESSONS  IN  ASTRONOMY 

the  aerolitic  meteors,  and  they  are  more  quickly  consumed 
and  therefore  do  not  penetrate  the  atmosphere  so  deeply. 

323.  Brightness,  Material,  and  Mass.  —  Now  and  then 
.a  shooting-star  rivals  Jupiter  or  even  Venus  in  bright- 
ness. A  considerable  number  are  like  first-magnitude 
stars,  but  the  great  majority  are  faint.  The  bright  ones 
generally  leave  trains.  Occasionally  it  has  been  possible 
to  get  a  "snap  shot,"  so  to  speak,  at  the  spectrum  of  a 
meteor,  and  in  it  the  bright  lines  of  sodium  and  magne- 
sium (probably)  are  fairly  conspicuous  among  many  others 
which  cannot  be  identified  by  such  a  hasty  glance. 

Since  these  bodies  are  consumed  in  the  air,  all  that  we 
can  hope  to  get  of  their  material  is  their  "  ashes." 

In  most  places  its  collection  and  identification  is,  of  course,  hope- 
less ;  but  the  Swedish  naturalist  Nordenskiold  thought  that  it  might 
be  found  in  the  polar  snows.  In  Spitzbergen  he  therefore  melted 
several  tons  of  snow,  and  on  filtering  the  water  he  actually  detected 
in  it  a  sediment  containing  minute  globules  of  oxide  and  sulphide 
of  iron.  Similar  globules  have  also  been  found  in  the  products  of 
deep-sea  dredging.  They  may  be  meteoric  ;  but  what  we  now  know 
of  the  distance  to  which  smoke  and  fine  volcanic  dust  is  carried 
by  the  wind  makes  it  not  improbable  that  they  may  be  of  purely 
terrestrial  origin. 

We  have  no  way  of  determining  the  exact  mass  of  a 
shooting-star  ;  but  from  the  light  it  emits,  as  seen  from  a 
known  distance,  an  approximate  estimate  can  be  formed, 
since  we  know  roughly  how  much  energy  corresponds  to 
the  production  of  a  given  amount  of  light.  It  is  likely, 
on  the  whole,  that  an  ordinary  meteor  and  a  good  elec- 
tric incandescent  lamp  do  not  differ  widely  in  what  is 
called  their  "luminous  efficiency,"  i.e.^  the  percentage  of 
their  total  energy  which  is  converted  into  visible  light. 


METEORIC   SHOWERS 


287 


Calculations  on  this  basis  indicate  that  ordinary  shooting- 
stars  are  very  minute,  weighing  only  a  small  fraction  of  an 
ounce,  —  from  less  than  a  grain  up  to  fifty  or  one  hundred 
grains  for  a  very  large  one.  Still  this  is  hardly  certain ; 
the  estimates  of  some  investigators  would  make  them 
considerably  larger. 

324,    Meteoric  Showers. — There  are  occasions  when  these 
bodies,  instead  of  showing  themselves  here  and  there  in 


FIG.  78.— The  Meteoric  Kadiant  in  Leo,  Nov.  13, 1867 

the  sky  at  intervals  of  several  minutes,  appear  in  showers 
of  thousands  ;  and  at  such  times  they  do  not  move  at 
random,  but  all  their  paths  diverge  or  radiate  from  a  single 
point  in  the  sky,  known  as  the  radiant;  i.e.,  their  paths 
produced  backwards  all  pass  through  this  point,  though 
they  do  not  usually  start  there.  Meteors  which  appear 


288  LESSONS  IN  ASTRONOMY 

near  the  radiant  are  apparently  stationary,  or  describe 
paths  which  are  very  short,  while  those  in  the  more 
distant  regions  of  the  sky  pursue  long  courses.  The 
radiant  keeps  its  place  among  the  stars  nearly  unchanged 
during  the  whole  continuance  of  the  shower,  and  the 
shower  is  named  according  to  the  place  of  the  radiant. 
Thus,  we  have  the  "  Leonids,"  or  meteors  whose  radiant  is 
the  constellation  of  Leo,  the  "  Andromedes  "  (or  Bielids), 
the  "  Perseids,"  the  "  Lyrids,"  etc. 

Fig.  78  represents  the  tracks  of  a  large  number  of  the  Leonids  of 
1867,  showing  the  position  of  the  radiant  near  Zeta  Leonis. 

The  radiant  is  explained  as  a  mere  effect  of  perspective. 
The  meteors  are  all  moving  in  lines  nearly  parallel  with 
each  other  when  encountered  by  the  earth,  and  the  radi- 
ant is  simply  the  perspective  "vanishing  point"  of  this 
system  of  parallels.  Its  position  depends  entirely  on 
the  direction  of  the  motion  of  the  meteors  with  respect 
to  the  earth.  For  various  reasons,  however,  the  paths 
of  the  meteors,  after  they  enter  the  air,  are  not  exactly 
parallel,  and  in  consequence  the  radiant  is  not  a  mathe- 
matical point,  but  a  "spot"  in  the  sky,  often  covering  an 
area  of  3°  or  4°  square. 

Probably  the  most  remarkable  of  all  the  meteoric  showers 
that  ever  occurred  was  that  of  the  Leonids,  on  Nov.  12, 
1833.  The  number  of  meteors  at  some  stations  was  esti- 
mated as  high  as  100,000  an  hour  for  five  or  six  hours. 
"  The  sky  was  as  full  of  them  as  it  ever  is  of  snowflakes 
in  a  storm." 

325.  Dates  of  Meteoric  Showers. — Such  meteoric  showers 
are  caused  by  the  earth's  encounter  with  a  swarm  of  little 


DATES  OF  METEORIC  SHOWERS  289 

• 

meteors,  and  since  this  swarm  pursues  a  regular  orbit 
around  the  sun,  the  earth  can  meet  it  only  when  she  is  at 
the  point  where  her  orbit  cuts  this  path.  The  encounter, 
therefore,  must  always  happen  on  or  near  the  same  day 
of  the  year,  except  as  in  time  the  meteoric  orbits  shift 
their  positions  on  account  of  perturbations.  The  Leonid 
showers,  therefore,  appear  about  November  15,  and  the 
Andromedes  about  the  27th  or  28th  of  the  same  month. 

But  the  Leonids  since  1800  have-changed  their  date  from  Novem- 
ber 12  to  November  15,  and  the  Andromedes  from  November  27 
to  November  23  since  1872,  —  the  effect  of  disturbance  by  the 
planets. 

In  some  cases  the  metebrs  are  distributed  along  their 
whole  orbit,  forming  a  sort  of  elliptical  ring  and  are 
rather  widely  scattered.  In  that  case  the  shower  recurs 
every  year  and  may  continue  for  several  weeks,  as  is  the 
case  with  the  Perseids,  which  appear  in  early  August. 
On  the  other  hand,  the  flock  may  be  concentrated,  and 
then  the  shower  will  occur  only  when  the  earth  and  the 
meteor  swarm  both  arrive  at  the  orbit-crossing  together. 
This  is  the  case  with  both  the  Leonids  and  the  Androm- 
edes. The  showers  then  occur,  not  every  year,  but  only 
at  intervals  of  several  years,  though  always  near  the  same 
day  of  the  month.  For  the  Leonids  the  interval  is  about 
thirty-three  years,  and  for  the  Bielids  about  thirteen  years, 
though  in  this  case  there  are  some  intermediate  showers, 
as  in  1898. 

326.  The  meteors  which  belong  to  the  same  group  have 
a  marked  family  resemblance.  The  Perseids  are  yellow 
and  move  with  medium  velocity.  The  Leonids  are  very 
swift  (we  meet  them),  and  they  are  of  a  bluish  green  tint, 


290  LESSONS  IN  ASTRONOMY 

i 

with  vivid  trains.  The  Bielids  are  sluggish  (they  over- 
take the  earth),  are  reddish,  being  less  intensely  heated 
than  the  others,  and  usually  have  only  feeble  trains. 
During  these  showers  no  sound  is  heard,  no  sensible  heat 
perceived,  nor  do  any  masses  of  matter  reach  the  ground ; 
with  one  exception,  however,  that  on  Nov.  27,  1885,  a 
piece  of  meteoric  iron  fell  at  Mazapil,  in  northern  Mexico, 
during  the  shower  of  Andromedes,  which  occurred  that  even- 
ing. The  coincidence  may  be  accidental,  but  is  certainly 
interesting.  Some  high  authorities  speak  confidently  of 
this  piece  of  iron  as  a  piece  of  Biela's  comet  itself ;  and 
this  brings  us  to  one  of  the  most  important  astronomical 
discoveries  of  the  last  half-century. 

327.  The  Connection  between  Comets  and  Meteors.  —  At 
the  time  of  the  great  meteoric  shower  of  1833,  Professors 
Olmsted  and  Twining  of  New  Haven  were  the  first  to 
recognize  the  "  radiant "  and  to  point  out  its  significance 
as  indicating  that  the  meteors  must  be  members  of  a  swarm 
of  bodies  revolving  around  the  sun  in  a  permanent  orbit. 
In  1864  Professor  Newton  of  New  Haven,  taking  up  the 
subject  anew,  showed  by  an  examination  of  the  old  records 
that  there  had  been  a  number  of  great  meteoric  showers 
about  the  middle  of  November,  at  intervals  of  thirty- 
three  or  thirty-four  years,  and  he  predicted  confidently 
the  repetition  of  the  shower  on  Nov.  13  or  14,  1866.  It 
occurred  as  predicted  and  was  observed  in  Europe;  and 
it  was  followed  by  another  in  1867,  which  was  visible  in 
America,  the  meteoric  swarm  being  extended  in  so  long  a 
procession  as  to  require  more  than  two  years  to  cross  the 
earth's  orbit.  The  researches  of  Newton  and  Adams 
showed  that  the  flock  was  moving  in  a  long  ellipse  with  a 


RELATION  BETWEEN  COMETS  AND  METEORS     291 


period  of  thirty-three  years.  Another  shower  was  pretty 
confidently  expected  in  1899  or  1900,  but  failed  to  appear; 
in  1901  there  was,  however,  a  well-marked,  but  not  very 
abundant,  display  on  the  night  of  November  14-15.1  The 
failure  to  appear  as  expected  is  ascribed  to  the  perturba- 
tions produced  by  Jupiter  and  Saturn  since  1866. 

328.    Identification  of  Meteoric  and  Cometary  Orbits.— 
Within  a  few  weeks  after  the  shower  of  1866  it  was  found 


FIG.  79.  —  Orbits  of  Meteoric  Swarms 

that  the  orbit  pursued  by  these  meteors  was  identical  with 
that  of  a  comet,  known  as  Tempel's,  which  had  been  visible 
about  a  year  before ;  and  about  the  same  time  Schiaparelli 
showed  that  the  Perseids,  or  August  meteors,  move  in 
an  orbit  identical  with  that  of  the  bright  comet  of  1862. 
Now  a  single  coincidence  might  be  accidental,  but  hardly 

1  Similar  minor  showers  occurred  in  1902,  1903,  and  1904. 


292 


LESSONS  IN  ASTRONOMY 


two.  Five  years  later  came  the  shower  of  Andromedes, 
following  in  the  track  of  Bieia's  comet,  and  among  the 
more  than  a  hundred  distinct  meteor  swarms  now  rec- 
ognized Professor  Alexander  Herschel  finds  five  others 
which  are  similarly  related  each  to  its  special  comet.  It 
is  no  longer  possible  to  doubt  that  there  is  a  real  and 


u=place  of  Uranus  126  A.D. 


FIG.  80.  —  Origin  of  the  Leonids 

close  connection  between  these  comets  and  their  attendant 
meteors.  Fig.  79  represents  four  of  the  orbits  of  these 
cometo-meteoric  bodies. 

329,  Nature  of  the  Connection.  —  This  cannot  be  said  to 
be  ascertained.  In  the  case  of  the  Leonids  and  Andro- 
medes the  meteoric  swarm  follows  the  comet,  but  this 
does  not  seem  to  be  so  in  the  case  of  the  Perseids,  which 
scatter  along  more  or  less  abundantly  every  year.  The 
prevailing  belief  is  that  the  comet  itself  is  only  the  thickest 


THE  METEO1UT1C   HYPOTHESIS  293 

part  of  the  meteoric  swarm,  and  that  the  clouds  of  meteors 
scattered  along  its  paths  are  the  result  of  its  disintegration  ; 
but  this  is  by  no  means  certain. 

It  is  easy  to  show  that  if  the  comet  really  is  such  a  swarm  it  must 
at  each  return  to  perihelion  gradually  break  up  more  and  more,  and 
disperse  its  constituent  particles  along  its  path  until  the  compact 
swarm  has  become  a  diffuse  ring.  The  longer  the  comet  has  been 
moving  around  the  sun,  the  more  uniformly  the  particles  will  be  dis- 
tributed. The  Perseids,  therefore,  are  supposed  to  have  been  in  the 
system  for  a  long  time,  while  the  Leonids  and  Andromedes  are 
believed  to  be  comparatively  new-comers.  Leverrier,  indeed,  has  gone 
so  far  as  to  indicate  the  year  126  A.D.  as  the  time  at  which  Uranus 
captured  Tempel's  comet  and  brought  it  into  the  system,  as  illus- 
trated by  Fig.  80.  But  the  theory  that  meteoric  swarms  are  the 
product  of  cometary  disintegration  assumes  the  premise  that  comets 
enter  the  system  as  compact  clouds,  which,  to  say  the  least,  is  not 
yet  certain. 

330.  Lockyer's  Meteoritic  Hypothesis.  —  Recently  Sir  Norman 
Lockyer  has  been  greatly  enlarging  the  astronomical  importance  of 
meteors.  The  probable  meteoritic  constitution  of  the  zodiacal  light, 
as  well  as  of  Saturn's  rings,  and  of  the  comets,  has  long  been 
recognized ;  but  he  goes  much  farther,  and  maintains  that  all  the 
heavenly  bodies  are  either  meteoric  swarms,  more  or  less  condensed, 
or  the  final  products  of  such  condensation.  Upon  this  hypothesis  he 
attempts  to  explain  the  evolution  of  the  planetary  system,  the  phe- 
nomena of  variable  and  colored  stars,  the  various  classes  of  stellar 
spectra,  and  the  forms  and  structure  of  the  nebulae,  —  indeed  pretty 
much  everything  in  the  heavens  from  the  Aurora  Borealis  to  the 
sun.  As  a  "working  hypothesis,"  his  theory  is  unquestionably 
important  and  has  attracted  much  attention,  but  it  encounters  serious 
difficulties  in  many  of  its  details. 


CHAPTER   XI 

THE  STARS 

Their  Nature,  Number,  and  Designation  —  Star-Catalogues  and  Charts  — 
Proper  Motions  and  the  Motion  of  the  Sun  in  Space  —  Stellar  Parallax  — 
Star  Magnitudes— Variable  Stars  —  Stellar  Spectra. 

331.  The  solar  system  is  surrounded  by  an  immense  void 
peopled  only  by  stray  meteors.     The  nearest  star,  so  far  as 
our  present  knowledge  goes,  is  one  whose  distance  is  more 
than  200,000  times  as  great  as  our  distance  from  the  sun,  — 
so  remote  that  from  it  the  sun  would  look  no  brighter  than 
the  Pole-star,  and  no  telescope  yet  constructed  would  be 
able  to  show  a  single  one  of  all  the  planets.     As  to  the 
nature  of  the  stars,  their  spectra  indicate  that  they  are 
bodies   resembling   our   sun,    that   is,    incandescent,    and 
each  shining  with  its  own  peculiar  light.     Some,  are  larger 
and  hotter  than  the  sun,  others  smaller  and  cooler;  some, 
perhaps  large,  but  hardly  luminous  at  all.     They  differ 
enormously  among  themselves,  not  being,  as  once  thought, 
as  much  alike  as  individuals  of  the  same  race,  but  differing 
as  widely  as  flies  from  elephants. 

332.  Number  of  Stars.  —  Those  which  are  visible  to  the 
eye,  though  numerous,   are   by  no   means   countless.     If 
we  take  a  limited  region,   the  bowl   of  the   Dipper  for 
instance,  we  shall  find  that  the  number  we  can  see  within 
it   is  not  very  large,  —  hardly  a   dozen.     In  the   whole 
celestial  sphere  the  number  of  stars  bright  enough  to  be 

294 


THE  CONSTELLATIONS  295 

distinctly  seen  by  an  average  eye  is  only  between  6000  and 
7000,  even  in  a  perfectly  clear  and  moonless  sky;  a  little 
haze  or  moonlight  will  cut  down  the  number  fully  one-half. 
At  any  one  time  not  more  than  2000  or  2500  are  fairly 
visible,  since  near  the  horizon  the  small  stars  (which  are 
vastly  the  more  numerous)  all  disappear.  The  total  number 
which  could  be  seen  by  the  ancient  astronomers  well  enough 
to  be  observable  with  their  instruments  is  not  quite  1100. 
With  even  the  smallest  telescope,  however,  the  number 
is  enormously  increased.  A  common  opera-glass  brings 
out  at  least  100,000,  and  with  a  2^-inch  telescope  Arge- 
lander  made  his  Durchmusterung  of  the  stars  north  of  the 
equator,  more  than  300,000  in  number.  The  Yerkes  tele- 
scope, 40  inches  in  diameter,  probably  makes  visible  at 
least  100,000000. 

333.  Constellations.  —  The  stars  are  grouped  in  so-called 
"  constellations,"   many  of  which  are  extremely  ancient. 
All  but  one  of  those  of  the  zodiac  and  most  of  those  near 
the  north  pole  antedate  history.     Their  names  are,  for  the 
most  part,  drawn  from  the  Greek  and  Roman  mythology, 
many  of  them  being  connected  in  some  way  or  other  with 
the  Argonautic  expedition.     In  some  cases  the  eye,  with 
the  help  of  a  lively  imagination,  can  trace  in  the  arrange- 
ment of  the  stars  a  vague  resemblance  to  the  object  which 
gives  the  name  to  the  constellation,  but  generally  no  reason 
is  obvious  for  either  name  or  boundaries. 

We  have  already,  in  Chap.  II,  given  a  brief  description 
of  those  constellations  which  are  visible  in  the  United 
States,  with  maps  and  directions  for  tracing  them. 

334,  Designation  of  the  Stars.  —  In  Sec.  24  we  have 
already   indicated  the    different   methods    by  which   the 


296  LESSONS  IN  ASTRONOMY 

brighter  stars  are  designated,  —  by  proper  names,  position 
in  the  constellation,  or  by  letters  of  the  Greek  and  Roman 
alphabets.  But  these  methods  do  not  apply  to  the  tele- 
scopic stars,  at  least  to  any  considerable  extent.  Such 
stars  we  identify  by  their  catalogue  number,  that  is,  we 
refer  to  them  as  number  so-and-so  in  some  star-catalogue. 
Thus,  LI.,  21,185  is  read  "Lalande,  21,185,"  and  means 
the  star  so  numbered  in  Lalande's  catalogue.  At  present 
more  than  1,000000  stars  are  catalogued,  so  that,  except 
in  the  Milky  Way,  every  star  visible  in  a  three-inch 
telescope  can  be  found  and  identified. 

Of  course  all  the  bright  stars  which  have  names  have 
letters  also  and  are  sure  to  be  found  in  every  catalogue 
which  covers  their  part  of  the  heavens.  A  conspicuous 
star,  therefore,  has  usually  many  "  aliases,"  and  sometimes 
great  care  is  necessary  to  avoid  mistakes  on  this  account. 

335.  Star-catalogues  are  carefully  arranged  lists  of  stars, 
giving  their  positions  (i.e.,  their  right  ascensions  and  decima- 
tions, or  latitudes  and  longitudes)  for  a  given  date,  usually 
also  indicating  their  so-called  magnitudes  or  brightness, 
and  often  giving  still  other  data.  The  earliest  of  these 
star-catalogues  was  made  about  125  B.C.  by  Hipparchus  of 
Bithynia,  the  first  of  the  world's  great  astronomers,  and 
gives  the  latitudes  and  longitudes  of  1080  stars.  This 
catalogue  was  republished  by  Ptolemy  250  years  later,  the 
longitudes  being  corrected  for  precession;  and  during 
the  Middle  Ages  several  other  catalogues  were  made  by 
Arabic  astronomers  and  those  that  followed  them.  The 
last  before  the  invention  of  the  telescope  was  that  of 
Tycho  Brahe,  about  1580,  containing  1005  stars.  The 
modern  catalogues  are  numerous ;  some,  like  Argelander's 


STAR-CATALOGUES  AND  CHARTS  297 

Durchmusterung,  give  the  places  of  a  great  number  of  stars 
rather  roughly,  merely  as  a  means  of  ready  identification. 
Others  are  "catalogues  of  precision,"  like  the  Pulkowa 
and  Greenwich  catalogues,  which  give  the  places  of  only 
a  few  hundred  so-called  "  fundamental "  stars  determined 
as  accurately  as  possible,  each  star  by  itself.  Finally,  we 
have  the  so-called  "zones,"  which  give  the  place  of  many 
thousands  of  stars  determined  accurately,  but  not  independ- 
ently ;  that  is,  their  positions  are  determined  by  reference 
to  the  fundamental  stars  in  the  same  region  of  the  sky. 

336.  Mean  and  Apparent  Places  of  the  Stars.  —  The  modern 
star-catalogue  contains  the  mean  right  ascension  and  declination  of 
its  stars  at  the  beginning  of  some  designated  year,  i.e.,  the  place  the 
star  would  occupy  if  there  were  no  nutation  or  aberration  (Sec,  126, 
and  Appendix,  435).     To  get  the  actual  (apparent)  right  ascension 
and  declination  of  a  star  for  some  given  date,  which  is  what  we 
always  want  in  practice,  the  catalogue  place  must  be  "  reduced  "  to 
that  date,  i.e.,  it  must  be  corrected  for  precession,  etc.     The  opera- 
tion is  an  easy  one  with  modern  formulae  and  tables,  but  tedious 
when  many  stars  are  to  be  dealt  with. 

337.  Star  Charts  and  Stellar  Photography.  —  For  some 
purposes  accurate  star  charts  are  even  more  useful  than 
catalogues.     The  old-fashioned  and  laborious  way  of  mak- 
ing such  charts  was  by  "plotting"  the  results  of   zone 
observations,  but  at  present  it  is  being  done,  by  means  of 
photography,  vastly  better  and  more  rapidly.     A  coopera- 
tive international  campaign  is  now  in  progress,  the  object 
of  which  is  to  secure  a  photographic  chart  of  all  the  stars 
down  to  the  fourteenth  magnitude.     Eighteen  different 
observatories  have  participated  in  the  work  which  is  now 
well    advanced,    although    its    completion  will    probably 
require  several  years  more. 


298 


LESSONS  IN  ASTRONOMY 


One  of  the  most  remarkable  things  about  the  photo- 
graphic method  is  that  there  appears  to  be  no  limit  to  the 
faintness  of  the  stars  that  can  be  photographed  with  a 
good  instrument.  By  increasing  the  time  of  exposure, 

smaller  and  smaller  stars 
are  continually  reached. 
With  the  ordinary  plates 
and  exposure-times  not 
exceeding  twenty  min- 
utes, it  is  now  possible 
to  get  distinct  photo- 
graphs of  stars  that  the 
eye  cannot  possibly  see 
with  the  same  tele- 
scope. 

Fig.  81  represents  the 
photographic  telescope 
(fourteen  inches  diame- 
ter and  eleven  f eet  focus, 
of  the  Paris  Observa- 
tory). The  other  instru- 
ments engaged  in  the 
star-chart  campaign  are 
substantially  like  it  in 


FIG.  81.  —  Photographic  Telescope  of  the 
Paris  Observatory 


diameter  and  length,   though  differing  more  or  less   in 
mounting  and  in  minor  details. 

Until  very  recently  the  most  powerful  instrument  of  this  class  was 
the  Bruce  photographic  telescope,  which  has  a  four-lens  object-glass 
of  twenty-four  inches  diameter  and  eleven  feet  focus,  taking  plates 
eighteen  inches  square.  It  belongs  to  the  observatory  of  Harvard 
College,  but  for  some  years  has  been  at  Arequipa,  Peru.  Within 


PROPER  MOTION  299 

the  last  two  or  three  years,  however,  other  photographic  telescopes 
of  equal  or  greater  power  have  been  mounted  at  Greenwich,  the 
Cape  of  Good  Hope,  Meudon,  and  Potsdam;  the  last  has  a  photo- 
graphic object-glass  of  31  £  inches  diameter. 

STAR  MOTIONS 

338.  The  stars  are  ordinarily  called  "  fixed,"  in  distinc- 
tion from  the  planets,  or  "  wanderers,"  because  they  keep 
their  positions  and  configurations  sensibly  unchanged  with 
respect  to  each  other  for  long  periods  of  time.     Delicate 
observations,  however,  demonstrate  that  the  fixity  is  not 
absolute,  but  that  the  stars  are  really  in  motion.     More- 
over, by  the  spectroscope,  their  rate  of  motion  towards  or 
from  the  earth  can  in  some  cases  be  approximately  meas- 
ured.    In  fact,  it  appears  that  the  velocities  of  the  stars 
are  of  the  same  order  as  those  of  the  planets:  they  are 
flying  through  space  far  more  swiftly  than  cannon-balls, 
and  it  is  only  because  of  their  enormous  distance  from  us 
that  they  appear  to  change  their  positions  so  slowly. 

339.  Proper  Motion.  —  If  we  compare  a  star's  position 
(right  ascension  and  declination)  as  determined  to-day  with 
that  observed   100  years    ago,  it  will  always    be  found 
to  have  changed  considerably.     The  difference  is  due  in 
the  main  to  precession  (Sec.  125) ;  but  after  allowing  for 
all  such  merely  apparent  motions  of  a  star,  it  generally 
turns  out  that  during  a  century  the  star  has  really  altered 
its  place  more  or  less  with  reference  to  others  near  it,  and 
this  shifting  of  its  place  is  called  its  "  proper  motion."     Of 
two  stars  side  by  side  in  the  same  telescopic  field  of  view 
the  proper  motions  may  be  directly  opposite,  while,  of 
course,  the  apparent  motions  will  be  sensibly  the  same. 


300  LESSONS  IN  ASTRONOMY 

Even  the  largest  of  these  proper  motions  is  very  small. 
For  many  years  the  so-called  "  runaway  star,"  1830  Groom- 
bridge,  headed  the  list  with  its  annual  drift  of  7".  But 
in  1898  it  was  superseded  by  a  little  star  designated  as 
"C.  Z.  (Cordova  Zones),  Hour  V,  No.  243,"  which  has 
a  proper  motion  of  8".  7  yearly,  and  in  1916  a  faint  star 
in  Ophiuchus  was  found  by  Barnard  to  change  its  posi- 
tion 10".4  a  year.  None  of  these  stars  is  visible  to  the 
naked  eye. 

About  a  dozen  stars  are  known  to  have  an  annual  proper 
motion  exceeding  3",  and  about  200,  so  far  as  known  at 
present,  exceed  V.  The  proper  motions  of  the  bright 
stars  average  higher  than  those  of  the  faint,  as  might  be 
expected,  since,  on  the  average,  the  bright  ones  are  prob- 
ably nearer.  For  the  first-magnitude  stars,  the  average 
is  about  \"  annually,  and  for  the  sixth-magnitude  stars, 
the  smallest  visible  to  the  naked  eye,  it  appears  to  be 
about  sV". 

Motions  of  this  kind  were  first  detected  in  1718  by  Halley,  who 
found  that  since  the  time  of  Hipparchus  the  star  Arcturus  had 
moved  towards  the  south  nearly  a  whole  degree,  and  Sirius  about 
half  as  much. 

340.  Velocity  of  Star  Motions.  —  The  proper  motion  of 
a  star  gives  us  very  little  knowledge  as  to  the  star's  real 
motion  in  miles  per  second.  The  proper  motion  is  derived 
from  the  comparison  of  star-catalogues  of  different  dates, 
and  is  only  the  value  in  seconds  of  arc  of  that  part  of  its 
motion  which  is  perpendicular  to  the  line  of  sight.  A  star 
moving  straight  towards  us  or  from  us  has  no  proper 
motion  at  all,  i.e.,  no  change  of  apparent  place  which  can 
be  detected  by  comparing  observations  of  its  position. 


VELOCITY  OF  STAR  MOTION  301 

We  can,  however,  in  some  cases  fix  a  minor  limit  to  the 
velocity  of  a  star.  We  know,  for  instance,  that  the  dis- 
tance of  the  star,  1830  Groombridge,  is  certainly  not  less 
than  1,400000  "astronomical  units,"  and,  therefore,  since 
its  yearly  path  subtends  an  angle  of  7"  at  the  earth,  the 
length  of  the  path  must  at  least  equal  48  astronomical 
units  a  year,  which  corresponds  to  a  velocity  of  over 
140  miles  a  second.  The  real  velocity  must  be  more  than 
this,  but  how  much  greater  we  cannot  determine  until  we 
know  how  much  the  star's  distance  exceeds  1,400000  units, 
and  also  how  fast  it  is  moving  towards  or  from  us. 

In  many  cases  a  number  of  stars  in  the  same  region 
of  the  sky  have  a  motion  practically  identical,  making  it 
almost  certain  that  they  are  real  neighbors  and  in  some 
way  connected,  —  probably  by  community  of  origin.  In 
fact,  it  seems  to  be  the  rule  rather  than  the  exception  that 
stars  which  are  apparently  near  each  other  are  real  com- 
rades ;  they  show,  as  Miss  Clerke  expresses  it,  a  distinctly 
"  gregarious  "  tendency. 

341.  Radial  Motion,  or  Motion  in  the  Line  of  Sight.  — 
Within  the  last  fifty  years  a  method l  has  been  developed 
by  which  any  swift  motion  of  a  star,  directly  towards  or 
from  us,  may  be  detected  by  means  of  the  spectroscope. 

If  a  star  is  approaching  us,  the  lines  of  its  spectrum  will 
apparently  be  shifted  towards  the  violet,  according  to 

1  It  is  not,  as  students  sometimes  think,  by  changes  in  the  apparent 
size  and  brightness  of  a  star.  Theoretically,  of  course,  a  star  which  is 
approaching  us  must  grow  brighter;  but  even  the  nearest  star  of  all, 
Alpha  Centauri  (Sec.  343),  is  so  far  away  that  if  it  were  coming  directly 
towards  us  at  the  rate  of  100  miles  a  second,  it  would  require  more  than 
8000  years  to  make  the  journey ;  so  that  in  a  century  its  brightness  would 
only  change  about  two  per  cent,  — far  too  little  to  be  noticed. 


302  LESSONS  IN  ASTRONOMY 

Doppler's  principle  (Sec.  179),  and  vice  versa  if  it  is 
receding  from  us.  Visual  observations  of  this  sort,  first 
made  by  Huggins  in  1868,  and  since  then  by  many  others, 
succeeded  in  demonstrating  the  reality  of  these  "radial 
motions"  (in  the  line  of  sight),  and  in  roughly  measur- 
ing some  of  them.  Later  (in  1888),  Vogel  of  Potsdam 
took  up  the  investigation  photographically,  and  obtained 
results  that  are  far  more  satisfactory  than  any  before 
reached.  He  photographed  the  spectrum  of  the  star  and 

the  spectrum  of   hydrogen  gas 
Red    (or  some  other  substance  whose 
lines    appear   in  the  star  spec- 
Spectrum  of  Rigd  trum)  together  upon  the   same 
FIG.  82. -Displacement  of  Hy     plate,  the  light  from  both  being 
Line  in  the  Spectrum  of  Beta    admitted  through  the  same  slit. 

Orionis  TJ,  .,  .  ,  . 

If  the  star  is  not  approaching  or 

receding,  its  lines  will  coincide  precisely  with  those  of 
the  comparison  spectrum  ;  otherwise  they  will  deviate  one 
way  or  the  other. 

Fig.  82  is  from  one  of  his  negatives  of  the  spectrum  of  Beta 
Orionis  (Rigel),  in  which  one  of  its  dark  lines  is  compared  with  the 
corresponding  bright  lines  in  the  spectrum  of  hydrogen.  The  dark 
line  of  the  stellar  spectrum  (bright  in  the  negative)  is  shifted  towards 
the  red  by  an  amount  which  indicates  that  at  the  time  the  star  was 
rapidly  receding. 

Still  more  recently  the  work  has  been  taken  up  at  several  observa- 
tories in  Europe  and  this  country  with  instruments  more  powerful 
than  Vogel  had  at  his  command,  and  with  great  success,  especially 
by  Keeler  and  Campbell  at  the  Lick  Observatory.  Fig.  83  is  enlarged 
from  a  recent  photograph  made  by  Frost  at  the  Yerkes  Observatory, 
showing  part  of  the  spectrum  of  Alpha  Persei  compared  with  that  of 
titanium ;  the  central  strip  is  the  spectrum  of  the  star,  and  it  will 


THE  SUN'S  WAY  303 

be  seen  that  its  dark  lines  are  shifted  towards  the  violet  with  respect 
to  the  bright  lines  of  the  metal,  indicating  that  the  star  and  earth 
were  approaching  each  other  at  the  rate  of  about  17  miles  a  second. 
(Only  a  few  of  the  lines  in  the  star  spectrum. are  due  to  titanium, 
and  not  all  the  lines  of  titanium  are  visible  in  the  star.) 

For  the  most  part  these  radial  motions  of  the  stars,  so 
far  as  ascertained,  range  between  zero  and  sixty  miles 
a  second,  with  still  higher  speeds  in  a  few  exceptional 
cases. 

342.  The  "  Sun's  Way."  —  The  proper  motions  of  the 
stars  are  due  partly  to  their  own  real  motions,  but  partly 
also  to  the  motion  of  the  sun,  which,  like  the  other  stars, 


12  3  4557 

FIG.  83.  —  Spectrum  of  Alpha  Persei,  compared  with  Titanium 
Frost,  Aug.  8,  1002 

is  traveling  through  space,  taking  with  it  its  planets.  Sir 
William  Herschel  was  the  first  to  investigate  and  determine 
the  direction  of  this  motion,  a  century  ago.  The  principle 
involved  is  this:  on  the  whole,  the  stars  must  appear  to 
drift  bodily  in  a  direction  opposite  to  the  real  motion  of 
the  solar  system. 

Those  in  that  quarter  of  the  sky  which  we  are  approach- 
ing open  out  from  each  other,  and  those  in  the  rear  close 
up  behind  us.  The  motions  of  individual  stars  may  lie  in 
all  possible  directions;  but  when  we  deal  with  them  by 
thousands  the  individual  is  lost  in  the  general,  and  the 
prevailing  drift  becomes  obvious. 


304  LESSONS  IN  ASTRONOMY 

A  number  of  different  determinations  of  the  point 
towards  which  the  sun's  motion  is  directed  have  been 
made  by  various  astronomers.  There  is  a  reasonable  and 
almost  surprising  accordance  of  results,  and  they  all  show 
that  the  sun  is  moving  towards  a  point  in  the  constella- 
tion of  Hercules,  having  a  right  ascension  of  about  267° 
(17h48m),  and  a  declination  of  about  32°  north.  This 
point  is  called  the  "  apex  of  the  sun's  way."  l  As  to  the 
velocity  of  this  motion  of  the  sun,  it  comes  out  as  about 
0".05  annually,  seen  from  the  average  distance  of  a  stand- 
ard sixth-magnitude  star.  This  would  make  the  sun's 
velocity  about  sixteen  miles  a  second. 

It  can,  however,  be  more  accurately  deduced  from  the 
spectroscopic  observations  of  radial  motion.  In  the  part 
of  the  heavens  toward  which  the  sun  is  moving  the  stars 
on  the  average  seem  to  approach,  and  in  the  opposite 
region  to  recede,  and  the  difference  of  the  two  averages  is 
twice  the  sun's  own  motion,  which  comes  out  about  eleven 
miles  a  second,  —  a  result  independent  of  all  uncertainty 
as  to  the  distances  of  the  stars. 


THE  PARALLAX  AND  DISTANCE  OF  STARS 

343.  When  we  speak  of  the  "  parallax  "  of  the  sun,  of 
the  moon,  or  of  a  planet,  we  always  mean  the  "  diurnal " 
or  "geocentric"  parallax  (Sec.  139);  i.e.,  the  apparent 
semi-diameter  of  the  earth  as  seen  from  the  body.  In  the 
case  of  a  star  this  kind  of  parallax  is  practically  nothing, 

1  If  there  are  any  predominant  drifts  among  the  stars  whose  motions 
form  the  basis  of  this  calculation,  as  recent  investigations  of  Kapteyn 
and  others  would  indicate,  this  computed  position  would  be  affected. 


ANNUAL  OR  HELIOCENTRIC  PARALLAX        305 


never  reaching  ^^^  of  a  second  of  arc.  The  expression 
"parallax  of  a  star"  always  refers,  on  the  contrary,  to 
its  "  annual  "  or  "  heliocentric  "  parallax  which  is  the  appar- 
ent semi-diameter  of  the  earth's  orbit,  as  seen  from  the 
star.  In  Fig.  84  the  angle  at  the  star  is  its  parallax. 

Even  this  heliocentric  parallax,  in  the  case  of  most 
stars,  is  far  too  small  to  be  detected  by  our  present 
instruments,  since  it  never  reaches  a  single  second  of  arc. 
But  in  a  few  instances  it  has  been  actually  measured  by 
operations  the  most  refined  and  difficult  in  the  whole  range 
of  astronomical  observation.  Alpha  Centauri,  which  is  our 
nearest  neighbor  so  far  as  yet  known,  has  a  parallax  of 

E 

FIG.  84.  —  The  Annual  Parallax  of  a  Star 

about  0".9  according  to  the  earlier  observers,  or  only  0".75 
according  to  the  latest  authorities.  There  are  but  four  or 
five  other  stars  at  present  known  which  have  a  parallax 
more  than  half  as  great  as  this,  and  perhaps  fifty  more 
for  which  a  sensible,  but  much  smaller  parallax  has  been 
detected.  (For  the  method  of  determining  stellar  parallax, 
see  Appendix,  Sees.  441-443.) 

344.  Unit  of  Stellar  Distance;  the  Light-Year.  —  The 
distances  of  the  stars  are  so  enormous  that  even  the  radius 
of  the  earth's  orbit,  the  "astronomical  unit"  hitherto 
employed,  is  far  too  small  for  convenience.  We  may  take 
as  the  unit  of  stellar  distance  the  parsec,  the  distance  of 
a  star  which  has  a  parallax  of  1",  or  we  may  use  the 


306  LESSONS  IN  ASTRONOMY 

so-called  light-year,  the  distance  light  travels  in  a  year.    This 
is  about  63,000  times  the  earth's  distance  from  the  sun. 

This  number  is  found  by  dividing  the  number  of  seconds  in  a  year 
by  499,  the  number  of  seconds  required  by  light  to  make  the  journey 
from  the  sun  to  the  earth  (Appendix,  Sec.  432). 

A  star  with  a  parallax  of  1"  is  at  a  distance  of  3.26 
light-years,  and  in  general  the  distance  in  light-years 

3  26 
equals  — '—,  where  prr  is  the  parallax  of  the  star  expressed 

in  seconds. 

So  far  as  can  be  judged  from  the  scanty  data,  it  appears 
that  few,  if  any,  stars  are  nearer  than  four  light-years  from 
the  solar  system;  that  the  naked-eye  stars  are  probably, 
for  the  most  part,  within  200  or  300  light-years ;  and  that 
many  of  the  remoter  stars  must  be  thousands,  or  even 
tens  of  thousands,  of  light-years  away. 

For  the  parallaxes  of  a  number  of  stars,  see  Table  V, 
Appendix. 

THE   LIGHT   OF   THE   STARS 

345,  Star  Magnitudes.  —  As  has  already  been  mentioned 
(Sec.  23),  Hipparchus  and  Ptolemy  arbitrarily  divided  the 
stars  into  six  "  magnitudes  "  according  to  their  brightness, 
the  stars  of  the  sixth  magnitude  being  those  which  are 
barely  perceptible  by  an  ordinary  eye,  while  the  first  class 
comprise  about  twenty  of  the  brightest.  After  the  inven- 
tion of  the  telescope  the  same  system  was  extended  to  the 
fainter  stars,  though  without  any  special  plan,  so  that 
the  magnitudes  assigned  to  telescopic  stars  by  different 
observers  are  very  discordant. 


THE  LIGHT-RATIO  OF  MAGNITUDES  307 

Heis  enumerates  the  stars  clearly  visible  to  the  naked  eye  north 
of  the  35th  parallel  of  south  declination,  as  follows : 

First  magnitude,  14  Fourth  magnitude,  313 

Second        "          48  Fifth  "  854 

Third          «         152  Sixth  «         2010 

Total,  3391 

It  will  be  noticed  how  rapidly  the  numbers  increase  for  the  smaller 
magnitudes.  Nearly  the  same  holds  good  also  for  the  telescopic  stars, 
though  below  the  tenth  magnitude  the  rate  of  increase  falls  off. 

346.  Light-Ratio  and  « Absolute  Scale "  of  Star  Mag- 
nitudes. —  The  scale  of  magnitudes  ought  to  be  such 
that  the  "  light-ratio,"  or  number  of  times  by  which  the 
brightness  of  any  star  exceeds  that  of  a  star  which  is 
one  magnitude  smaller,  should  be  the  same  throughout 
the  whole  extent  of  the  scale.  This  relation  was  roughly, 
but  not  accurately,  observed  by  the  older  astronomers..  In 
recent  years  photometric  measurements  have  been  made  of 
the  brightness  of  all  the  naked-eye  stars  visible  in  our 
latitude,  and  magnitudes  have  been  published  which  are 
based  upon  the  so-called  "  absolute  scale "  first  proposed 
by  Pogson  about  1850,  which  uses  a  light-ratio  equal  to 
the  fifth  root  of  100  (2.51  +) ;  i.e.,  upon  this  scale  a  star 
of  the  third  magnitude  is  2.51  times  brighter  than  one  of 
the  fourth,  one  of  the  fourth  2.51  times  as  bright  as  one 
of  the  fifth,  and  so  on. 

The  scale  is  being  extended  rapidly  to  the  fainter  stars. 

The  ratio  is  based  upon  an  old  determination  of  Sir  John  Her- 
schel,  who  found  that  the  average  first-magnitude  star  is  just  about 
a  hundred  times  as  bright  as  a  star  of  the  sixth  magnitude,  five 
magnitudes  fainter,  so  that  an  increase  of  Jive  in  the  "  magnitude  " 
corresponds  to  a  hundredfold  decrease  of  brightness. 


308  LESSONS  IN   ASTRONOMY 

On  this  scale  Altair  (Alpha  Aquilse)  and  Aldelaran 
(Alpha  Tauri)  may  be  taken  as  standard  first-magnitude 
stars,  while  the  Pole-star  and  the  two  Pointers  are  very 
nearly  of  the  standard  second  magnitude. 

Of  course,  in  indicating  the  brightness  of  stars  with  precision, 
fractional  numbers  must  be  used,  that  is,  we  have  stars  of  2.4 
magnitude,  etc. 

Stars  that  are  brighter  than  Aldebaran  or  Altair  have  their  bright- 
ness denoted  by  a  fraction,  or  even  by  a  negative  number  ;  thus  the 
absolute  magnitude^f  Vega  is  0.2,  and  of  Sirius  —  1.4.  The  neces- 
sity of  these  negative  and  fractional  magnitudes  for  bright  stars  is 
rather  unfortunate,  but  not  really  of  much  importance,  as  there  are 
too  few  of  them  to  cause  any  practical  inconvenience. 

347.  Magnitudes  and  Telescopic  Power.  —  If  a  good  telescope 
just  shows  a  star  of  a  certain  magnitude,  we  must  have  a  telescope 
with  its  aperture  larger  in  the  ratio  of  1.58  : 1,  in  order  to  show  stars 
one  magnitude  smaller  (1.58  =  V2.51).     A  tenfold  increase  in  the 
diameter  of  an  object-glass  theoretically  carries  the  power  of  vision 
just  five  magnitudes  lower. 

It  is  usually  estimated  that  the  twelfth  magnitude  is  the  limit  of 
vision  for  a  four-inch  glass.  It  would  require,  therefore,  a  forty-inch 
glass  to  reach  the  seventeenth  magnitude  of  the  absolute  scale. 

Our  space  does  not  permit  any  extended  discussion  of  the  photo- 
metric methods  by  which  the  brightness  of  stars  is  measured,  —  a 
subject  which  has  of  late  attracted  much  attention.  (See  General 
Astronomy,  Arts.  823-829.) 

348.  Starlight  compared  with  Sunlight.  —  Zollner  and 
others  have  endeavored  to  determine  the  amount  of  light2 

1  The  sun  on  this  scale  is  about  —  26.3  magnitude. 

2  The  stars  send  us  heat  also,  but  probably  the  ratio  of  stellar  heat  to 
solar  does  not  differ  much  from  that  of  starlight  to  sunlight.     If  so,  the 
heat  from  a  star  is  beyond  the  reach  of  any  ordinary  instrument.     Very 
recently,  however,  Professor  E.  F.  Nichols,  at  the  Yerkes  Observatory, 
with  a  new  "radiometer,"  has  obtained  distinct  and  measurable  heat 
effects  from  Arcturus  and  Vega. 


STARLIGHT  COMPARED   WITH   SUNLIGHT       309 

received  by  us  from  certain  stars,  as  compared  with  the 
light  of  the  sun.  According  to  him,  Sirius  gives  us  about 
YinnnfirffTnnr  as  mucn  light  as  the  sun  does,  and  Capella 
and  Vega  about  -%-Q-Q-Q-Q  ^-Q-O  o  o"o-  At  this  rate,  the  standard 
first-magnitude  star,  like  Altair,  should  give  us  about 
¥<JF<ro  W^^>  an(*  it  would  take,  therefore,  about  nine  mil- 
lion million  stars  of  the  sixth  magnitude  to  equal  the  sun. 
These  numbers,  however,  are  very  uncertain.  The  various 
determinations  for  Vega  vary  more  than  fifty  per  cent. 

Assuming  what  is  only  roughly  true,  that  Argelander's  magnitudes 
agree  with  the  absolute  scale,  it  appears  that  the  324,000  stars  of  his 
Durchmusterung,  all  of  them  north  of  the  celestial  equator,  give 
a  light  about  equivalent  to  240  or  250  first-magnitude  stars.  How 
much  light  is  given  by  stars  smaller  than  the  9£  magnitude  (which  was 
his  limit)  is  not  certain.  It  must  greatly  exceed  that  given  by  the 
larger  stars.  As  a  rough  guess,  we  may  estimate  that  the  total  star- 
light of  both  the  northern  and  southern  hemispheres  is  equivalent  to 
about  3000  stars  like  Vega,  or  1500  at  any  one  time.  According  to 
this,  the  starlight  on  a  clear  night  is  about  ^  of  the  light  of  a  full 
moon,  or  about  -SJ-Q-Q^-QTJV  that  of  sunlight.  Professor  NeM^comb's 
recent  estimate  of  the  total  starlight  is,  however,  only  about  one- 
fourth  as  large ;  the  data  do  not  warrant  any  exact  conclusion. 
More  than  ninety  per  cent  of  the  light  comes  from  stars  not  visible 
by  the  naked  eye. 

349.  Amount  of  Light  emitted  by  Certain  Stars.  —  When 
we  know  the  distance  of  a  star  in  astronomical  units  it  is 
easy  to  compute  the  amount  of  light  it  really  emits  as  com- 
pared with  that  given  off  by  the  sun.  It  is  only  necessary  to 
multiply  the  light  we  now  get  from  it  (expressed  as  a  fraction 
of  sunlight)  by  the  square  of  the  star's  distance  in  astro- 
nomical units.  Thus,  the  distance  of  Sirius  is  about  550,000 
units,  and  the  light  we  receive  from  it  is 


310  LESSONS  IK  ASTRONOMY 

of  sunlight.  Multiplying  this  fraction  by  the  square  of 
550,000,  we  find  that  Sirius  is  really  radiating  more  than 
forty  times  as  much  light  as  the  sun.  As  for  several  other 
stars  whose  distance  and  light  have  been  measured,  some 
turn  out  brighter,  and  some  darker,  than  the  sun.  The 
range  of  variation  is  very  wide,  and  in  brilliance  the  sun 
holds  apparently  about  a  medium  rank  among  its  kindred. 

350.  Why  the  Stars  differ  in  Brightness.  —  The  appar- 
ent brightness  of  a  star,  as  seen  from  the  earth,  depends 
both  on  its  distance  and  on  the  quantity  of  light  it  emits, 
and  the  latter  depends  on  the  extent  of  its  luminous  sur- 
face and  upon  the  brightness  of  that  surface.     As  Bessel 
long  ago  suggested,  "  there  may  be  as  many  dark  stars  as 
bright  ones." 

Taken  as  a  class,  the  bright  stars  undoubtedly  average 
nearer  to  us  than  the  fainter  ones  ;  and  just  as  undoubtedly 
they  also  average  larger  in  diameter  and  more  intensely 
luminous ;  but  when  we  compare  any  particular  bright 
star  with  another  fainter  one  we  can  seldom  say  to  which 
of  these  different  causes  it  owes  its  superiority.  We  can- 
not assert  that  the  faint  star  is  smaller,  or  darker,  or 
more  distant  than  that  particular  bright  star,  unless  we 
know  something  more  about  it  than  the  simple  fact  that 
it  is  fainter. 

351.  Dimensions  of  the  Stars.  —  The  stars  are  so  far 
away  that  their  apparent  diameters  are  altogether  too  small 
to  be  measured  by  any  known  form  of  micrometer.     The 
sun  at  the  distance  of  the  nearest  star  would  measure l  not 
quite  0".01  across.     Micrometers,  therefore,  do  not  help 

1This  does  not  refer,  of  course,  to  the  "spurious  disk"  of  the  star 
(Appendix,  Sec.  408),  which  is  many  times  larger. 


VARIABLE  STARS  311 

us  in  the  matter,  and  until  very  recently  we  were  abso- 
lutely without  any  positive  knowledge  as  to  the  real  size 
of  a  single  one  of  the  stars.  But  in  1889,  by  a  spectro- 
scopic  method  more  fully  explained  in  Sec.  360,  Vogel 
succeeded  in  showing  that  the  bright  variable  star,  Algol 
(Beta  Persei)  (Sec.  358),  must  have  a  diameter  of  about 
1,160000  miles,  while  its  invisible  companion  is  about 
840,000  miles  in  diameter,  or  just  about  the  size  of  the  sun. 

VARIABLE   STARS 

352.  Classes  of  Variables.  —  Many  stars  are  found  to 
change  their  brightness  more  or  less  and  are  known  as 
"variable."     They  may  be  classed  as  follows: 

I.  Stars  which  change  their  brightness  slowly  and  con- 
tinuously. 

II.  Those  that  fluctuate  irregularly. 

III.  Temporary  stars  which  blaze  out  suddenly  and  then 
disappear. 

IV.  Periodic  stars  of  the  type  of  "  Omicron  Ceti,"  usually 
having  a  period  more  or  less  irregular,  and  usually  of  several 
months. 

V.  Periodic  stars  having  short  periods,  with  a  continu- 
ous change  of  light. 

VI.  Periodic  stars  of  the  "Algol"  type,  in  which  the 
period  is  usually  short,  and  the  variation  is  like  what  might 
be  produced  if  the  star  were  periodically  "eclipsed"  by 
some  intervening  object. 

353.  Gradual  Changes.  —  The  number  of  stars  which  are 
certainly  known  to  be  gradually  changing  in  brightness  is 
surprisingly  small.     On  the  whole,  the  stars  present,  not 


312  LESSONS  IN  ASTRONOMY 

only  in  position,  but  in  brightness  also,  sensibly  the  same 
relations  as  in  the  catalogues  of  Hipparchus  and  Ptolemy. 

There  are,  however,  a  few  instances  in  which  it  can  hardly  be 
doubted  that  considerable  alteration  has  occurred,  even  within  the 
last  two  or  three  centuries.  Thus,  in  1610,  Bayer  lettered  Castor  as 
Alpha  Geminorum,  while  Pollux,  which  he  called  Beta  Geminorum, 
is  now  distinctly  brighter.  There  are  about  a  dozen  other  similar 
cases  known  and  a  much  larger  number  is  suspected. 

It  is  commonly  believed  that  a  considerable  number  of  stars  have 
disappeared  since  the  first  catalogues  were  made,  and  that  many  new 
ones  have  come  into  existence.  While  it  is  unsafe  to  deny  absolutely 
that  such  things  may  have  happened,  it  can  be  said,  on  the  other 
hand,  that  not  a  single  case  of  the  kind  is  certainly  known.  The  dis- 
crepancies between  the  older  and  newer  catalogues  are  nearly  all 
accounted  for  by  some  error  that  has  already  been  discovered. 

354.  Irregular  Fluctuations.  —  The  most  conspicuous  star 
of  the  second  class  is  Eta  Argus  (not  visible  in  the  United 
States).     It  varies  all  the  way  from  above  the  first  magni- 
tude (in  1843  it  stood  next  to  Sirius)  down  to  the  seventh 
magnitude  (invisible  to  the  eye).     This  has  been  its  status 
ever  since  1865,  though  some  years  ago  it  was  reported  as 
slightly  brightening.     Alpha  Orionis,  Alpha  Herculis,  and 
Alpha  Cassiopeise  behave  in  a  similar  way,  except  that  their 
variation  is  small,  never  reaching  an  entire  magnitude. 

355.  Temporary  Stars.  — There  are  several  well-authenti- 
cated instances  (and  a  number  of  others  more  or  less  doubt- 
ful) of  stars  which  have  blazed  up  'suddenly,  and  then 
gradually  faded  away.    (See  General  Astronomy,  Arts.  842- 
845.)    The  most  remarkable  of  these  is  that  known  as 
Tycho's  star,  which  appeared  in  the  constellation  of  Cassi- 
opeia (Sec.  28)  in  November,  1572,  was  for  some  days  as 
bright  as  Venus  at  her  best,  and  then  gradually  faded  away, 


TEMPORARY  STARS  313 

until  at  the  end  of  sixteen  months  it  became  invisible. 
(There  were  110  telescopes  then.)  It  is  not  certain  whether 
it  still  exists  as  a  telescopic  star ;  so  far  as  we  can  judge, 
it  may  be  any  one  of  half  a  dozen  which  are  near  the  place 
determined  by  Tycho. 

It  is  a  notable  and  probably  significant  fact,  though  as  yet  unex- 
plained, that  all  these  objects  have  appeared  in  or  within  a  few 
degrees  of  the  Milky  Way. 

A  temporary  star,  which  appeared  in  the  constellation 
Corona  Borealis,  in  May,  1866,  is  interesting  as  having 
been  the  first  spectroscopically  examined.  When  near  its 
brightest  (second  magnitude)  it  showed  the  same  bright 
lines  of  hydrogen  which  are  conspicuous  in  the  solar  promi- 
nences. Before  its  outburst  it  was  an  eighth-magnitude 
star  of  Argelander's  catalogue,  and  within  a  few  months 
it  returned  to  its  former  low  estate,  which  it  still  retains. 

Another  instance  is  that  of  a  sixth-magnitude  star,  which 
in  August,  1885,  suddenly  appeared  in  the  midst  of  the  great 
nebula  of  Andromeda  (Sec.  377).  It  showed  no  bright  lines 
in  its  spectrum  and  in  a  few  months  it  totally  disappeared, 
even  to  the  largest  telescopes. 

In  1892  a  star  of  magnitude  4J  appeared  in  the  con- 
stellation of  Auriga.  It  showed  what  is  now  known  to  be 
the  characteristic  spectrum  of  a  temporary  star,  a  combina- 
tion of  bright  and  dark  lines  of  hydrogen  and  helium,  the 
dark  lines  always  on  the  side  toward  the  violet.  It  is  thought 
possible  that  this  peculiar  spectrum  may  be  due  to  the 
effect  of  intense  explosive  pressures  in  the  luminous  gases. 
In  April  the  star  became  invisible,  but  brightened  up 
again  in  the  autumn,  and  then  showed  an  entirely  different 
spectrum  closely  resembling  that  of  a  nebula  (Sec.  380). 


314  LESSONS  IN  ASTRONOMY 

Later,  in  1902,  Campbell  reported  that  its  spectrum  had 
become  continuous,  the  object  having  apparently  become 
a  star  again. 

355*.  Nova  Persei.  —  A  recent  and  also  one  of  the 
most  remarkable  of  temporary  stars  is  that  first  seen  on 
Feb.  21,  1901,  when  it  was  already  as  bright  as  the  Pole- 
star.  Photographs  of  the  region  made  at  Cambridge  on 
the  19th  and  previous  dates  prove  that  on  the  19th  it 
must  still  have  been  fainter  than  the  twelfth  magnitude. 
On  the  24th  it  was  for  several  hours  the  brightest  star 
then  visible,  Sirius  alone  excepted,  having  increased  its 
brilliance  more  than  twenty-five  thousand  fold  within  five 
days.  It  faded  rapidly,  with  curious  oscillations  of  light, 
and  before  the  end  of  the  year  had  dropped  below  the 
range  of  the  eye.  It  is  now  visible  only  in  large  tele- 
scopes. Its  spectrum,  when  first  photographed  on  Feb- 
ruary 22,  was  simply  dark  lined,  resembling  that  of  the 
Orion  stars ;  but  by  the  24th  it  was  transfigured  and  had 
become  bright  lined  like  that  of  Nova  Aurigse.  It  then 
gradually  changed  into  the  nebular  type,  but  with  the 
peculiarity  that  its  lines  were  extremely  broad  and  hazy, 
and  still  preserve  this  character,  though  very  faint.  Sev- 
eral different  observers  have  found  that  its  proper  motion 
and  parallax  are  insensible,  its  distance  from  us  almost 
certainly  exceeding  a  hundred  light-years. 

Before  the  star  became  invisible  to  the  eye  an  extensive 
nebulosity  had  developed  around  it,  and  in  November  pho- 
tographs made  with  the  three-foot  reflector  of  the  Lick 
Observatory,  and  confirmed  by  others  from  the  Yerkes, 
showed  that  certain  knots  and  streaks  of  the  nebula  were 
apparently  moving  swiftly  away  from  the  central  star,  - 


LIGHT  CURVES  OF  VARIABLES 


315 


at  a  rate  of  several  thousand  miles  a  second  (!)  —  unless  the 
star  is  much  nearer  than  the  parallax  observations  permit 
us  to  assume.  At  present  the  explanation,  first  suggested 
by  Kapteyn,  is  generally,  though  not  universally,  accepted, 
—  that  the  motion  is  purely  apparent,  and  due  to  a 


FIG.  85.  —  Light  Curves  of  Variable  Stars 

progressive  illumination  of  denser  portions  of  the  nebula 
as  the  light  from  the  great  explosion  travels  outward 
186,000  miles  a  second.  This  would  make  the  distance 
of  the  star  about  three  hundred  light-years,  which  is  not 
at  all  improbable. 

A  brilliant  "Nova"  appeared  in  Aquila  June  8,  1918.  It  was 
nearly  as  bright  as  Vega  when  discovered,  the  next  night  rivaled 
Sirius,  then  gradually  faded. 

356.  Variables  of  the  "  Omicron  Ceti"  Type.  —  These, 
objects  behave  almost  exactly  like  a  temporary  star  in 
remaining  most  of  the  time  faint,  rather  suddenly  increasing 


816  LESSONS  IN  ASTRONOMY 

in  brightness,  and  then  gradually  fading  away;  but  they 
do  it  periodically.  Omicron  Ceti,  or  Mira  (i.e.,  "the 
wonderful")  is  the  type.  It  was  discovered  in  1596  and 
was  the  first  variable  star  known.  During  most  of  the 
time  it  is  of  the  ninth  magnitude;  but  at  intervals  of 
about  eleven  months  it  runs  up  to  the  fourth,  third,  or  even 
second  magnitude,  and  then  back  again,  the  whole  change 
occupying  about  three  hundred  days,  and  the  rise  being 
much  more  rapid  than  the  fall.  It  remains  at  its  maxi- 
mum about  a  week  or  ten  days.  The  maximum  bright- 
ness varies  very  considerably ;  and  its  period,  while  always 
about  eleven  months,  varies  to  the  extent  of  two  or  three 
weeks.  The  spectrum  of  the  star  when  brightest  is  very 
beautiful,  showing  a  large  number  of  intensely  bright  lines, 
some  of  which  are  due  to  hydrogen  and  helium.  Its  light 
curve  is  A  in  Fig.  85.1 

There  are  several  hundred  variables  of  this  class,  and 
many  of  them  have  periods  which  do  not  differ  very 
widely  from  a  year.  Most  of  the  periods,  however,  are 
more  or  less  irregular. 

357.  Class  V.  —  The  variables  of  this  class  change  their 
light  regularly  and  continuously,  with  an  average  range 
of  about  one  magnitude.  The  periods  are  short,  from 
several  hours  to  a  few  weeks.  Sometimes  the  light  curve 
is  like  that  of  Eta  Aquilse,  shown  in  B  of  Fig.  85,  the 
increase  in  brightness  being  much  more  rapid  than  the 
decrease;  sometimes,  as  in  the  case  of  Zeta  Geminorum, 
the  ascending  and  descending  branches  of  the  curve  are 
alike. 

1  The  light-curve  diagrams  are  not  drawn  to  scale,  and  make  no  pre- 
tensions to  exact  accuracy  ;  details  differ  for  each  star. 


EXPLANATION  OF  VARIABLES  317 

358.  The  " Algol' »  Type.  —  In  the  stars  of  Class  VI  the 
variation  is  precisely  the  reverse  of  that  in  Class  IV.    The 
star  remains  bright  for  most  of  the  time,  but  apparently 
suffers  a  periodical  eclipse.     The  periods  are  mostly  very 
short,  ranging  from  ten  hours  to  ten  days. 

Algol  (Beta  Persei)  is  the  type  star.  During  most  of 
the  time  it  is  of  the  second  magnitude,  and  it  loses  about 
five-sixths  of  its  light  at  the  time  of  obscuration.  The  fall 
of  brightness  occupies  about  4j  hours.  The  minimum 
lasts  about  20  minutes,  and  the  recovery  of  light  takes 
about  3^  hours.  The  period,  a  little  less  than  three  days,  is 
known  with  great  precision,  —  to  a  single  second  indeed,  — 
and  is  given  in  connection  with  the  light  curve  of  the  star 
in  Fig.  85.  At  present  the  period  seems  to  be  slowly 
shortening.  Above  ninety  variables  of  this  class  are  now 
known,  and  new  ones  are  continually  found. 

359.  Explanation  of  Variable  Stars.  — No  single  explana- 
tion will  cover  the  whole  ground.   As  to  progressive  changes, 
no  explanation  need  be  looked  for.     The  wonder  rather  is 
that  as  the  stars  grow  old  such  changes  are  not  more  rapid 
and  notable  than  they  are.    With  few  exceptions  there  has 
been  no  obvious  alteration  since  the  days  of  Ptolemy. 

As  for  irregular  changes,  no  sure  account  can  yet  be 
given.  Where  the  range  of  variation  is  small  (as  it  is  in 
most  cases)  one  thinks  of  spots  upon  the  surface  of  the 
star,  more  or  less  like  sun-spots ;  and  if  we  suppose  these 
spots  to  be  much  more  extensive  and  numerous  than  are 
the  sun-spots,  and  also  like  them  to  have  a  regular  period 
of  frequency,  and  also  that  the  star  revolves  upon  its  axis, 
we  find  in  the  combination  a  possible  explanation  of  a 
large  proportion  of  all  the  variable  stars. 


318  LESSONS  IN  ASTRONOMY 

For  the  temporary  stars  we  may  imagine  either  great 
eruptions  of  glowing  matter,  like  solar  prominences  on  an 
enormous  scale,  or,  with  Sir  Norman  Lockyer,  we  may 
imagine  that  they,  and  most  of  the  variable  stars,  are  only 
swarms  of  meteors,  rather  compact,  but  not  yet  having 
reached  the  condensed  condition  of  our  own  sun.  Out- 
bursts of  brightness  are,  according  to  him,  the  result  of 
collisions  between  such  swarms.  Stars  of  the  Mira  type, 
according  to  this  theory,  consist  of  two  such  swarms,  the 
smaller  revolving  around  the  larger  in  a  long  oval,  so  that 
once  in  every  revolution  it  brushes  through  the  outer  por- 
tions of  the  larger  one.  But  the  great  irregularity  in  the 
periods  of  variables  belonging  to  this  class  is  hard  to 
reconcile  with  a  true  orbital  revolution,  which  usually 
keeps  time  accurately. 

In  the  case  of  the  short-period,  "  punctual  variables,"  as 
Miss  Clerke  calls  them,  of  Class  V,  the  spectroscopic  phe- 
nomena in  many  instances  seem  to  indicate  the  mutual 
interaction  of  two  or  more  bodies  revolving  around  their 
common  center  of  gravity ;  this  is  certainly  the  case  with 
Beta  Lyrae.  Others  admit  of  simpler  explanation,  as  due 
to  the  rotation  of  a  body  of  irregular  form  or  having  large 
spots  on  its  surface. 

360.  Explanation  of  the  Algol  Type.  —  The  natural  and 
most  probable  explanation  of  the  behavior  of  these  stars  is 
that  the  periodical  darkening  is  produced  by  the  interposi- 
tion of  some  opaque  body  between  us  and  the  star. 

This  eclipse  theory,  first  proposed  by  Goodricke  a  hun- 
dred years  ago,  received  a  striking  confirmation  from  the 
spectroscopic  work  of  Vogel,  who,  in  1889,  found  by  the 
method  indicated  in  Sec.  341  that  about  seventeen  hours 


EXPLANATION  OF  ALGOL  319 

before  the  obscuration  Algol  is  receding  from  us  at  the 
rate  of  nearly  twenty-seven  miles  a  second,  while  seven- 
teen hours  after  the  minimum  it  approaches  us  at  the  same 
rate.  This,  is  just  what  it  ought  to  do  if  it  had  a  large 
dark  companion,  and  the  two  were  revolving  around  their 
common  center  of  gravity  in  an  orbit  nearly  edgewise  to 
the  earth.  When  the  dark  star  is  rushing  forward  to 
interpose  itself  between  us  and  Algol,  Algol  itself  must  be 
moving  backwards,  and  vice  versa  when  the  dark  star  is 
receding  after  the  eclipse.  Recently  it  has  been  proved  that 
the  companion  is  not  totally  dark,  but  that  there  is  a  very 
slight  reduction  of  light  halfway  between  minima,  when  the 
darker  star  is  eclipsed  by  the  brighter  one.  The  combined 
mass  of  the  two  is  about  two-thirds  that  of  the  sun,  and 
their  density  is  not  much  greater  than  that  of  cork.  Russell, 
and,  simultaneously,  Roberts  of  South  Africa,  have  shown 
that  the  phenomena  of  variables  of  this  class  determine  a 
maximum  limit  to  the  mean  density  of  the  pair ;  and  they 
find  in  all  cases  this  highest  possible  density  to  be  far  below 
that  of  the  sun.  These  stars  seem  to  be  hardly  denser  than 
clouds. 

361.  Number  and  Designation  of  Variables  and  their 
Range  of  Variation.  —  Mr.  Chandler's  catalogue  of  known 
variables,  with  its  later  supplements,  includes  393  objects, 
besides  a  considerable  number  of  suspected  variables. 

About  275  of  the  393  are  distinctly  periodic.  The  rest 
of  them  are,  some  irregular,  some  temporary,  and  in  respect 
to  many  we  have  not  yet  certain  knowledge  whether  the 
variation  is  or  is  not  periodic. 

Table  IV,  Appendix,  contains  a  list  of  the  principal 
naked-eye  variables  visible  in  the  United  States. 


320  LESSONS  IN  ASTRONOMY 

Such  variable  stars  as  had  not  names  of  their  own  before  their 
variability  was  discovered  are  at  present  generally  indicated  by  the 
letters  R,  S,  T,  etc. ;  i.e.,  R  Sagittarii  is  the  first  discovered  variable 
in  the  constellation  of  Sagittarius ;  S  Sagittarii  is  the  second,  etc. 

In  a  considerable  number  of  the  earlier  discovered  vari- 
ables the  range  of  brightness  is  from  two  to  eight  magni- 
tudes, that  is,  the  maximum  brightness  exceeds  the  minimum 
from  6  to  1000  times.  In  the  majority,  however,  the  range 
is  much  less,  —  only  a  fraction  of  a  magnitude. 

It  is  worth  noting  that  a  large  proportion  of  the  vari- 
ables, especially  those  of  Classes  IV  and  V,  are  reddish  in 
their  color.  This  is  not  true  of  the  Algol  type. 

Since  the  publication  of  Chandler's  last  catalogue  in  1896  there 
has  been  a  rapid  increase  in  the  number  of  known  variables,  largely 
as  the  result  of  the  examination  of  photographs  made  at  Arequipa 
on  different  dates.  The  total  number  known  at  the  present  time 
probably  exceeds  4000,  and  is  continually  growing.1 

The  most  remarkable  discovery  in  this  line,  however,  is  that  of 
multitudes  of  variables  in  certain  star  clusters.  The  clusters  known 
as  Messier  3,  Messier  5,  and  Omega  Centauri  are  especially  notable ; 
in  the  first,  132  variables  have  been  detected,  in  the  second,  85,  and 
in  the  last,  128.  The  changes  are  so  rapid  as  to  be  obvious  on 
photographs  taken  only  two  hours  apart. 

STAR   SPECTRA 

362.  As  early  as  1824  Fraunhofer  observed  the  spectra 
of  a  number  of  bright  stars  by  looking  at  them  with  a 
small  telescope  with  a  prism  in  front  of  the  object-glass. 
In  1864,  as  soon  as  the  spectroscope  had  taken  its  place  as 
a  recognized  instrument  of  research,  it  was  applied  to  the 
stars  by  Huggins  and  Secchi.  The  former  studied  very 
few  spectra,  but  very  thoroughly,  with  reference  to  the 
1  See  note  on  page  326. 


CLASSES   OF    STELLAR   SPECTRA 


321 


identification  of  the  chemical  elements  in  certain  stars. 
He  found  with  certainty  in  their  spectra  the  lines  of  sodium, 
magnesium,  calcium,  iron,  and  hydrogen,  and  more  or  less 
doubtfully  a  number  of  other  metals.  Secchi,  on  the 
other  hand,  examined  a  great  number  of  spectra,  less  in 
detail,  but  with  reference  to  a  classification  of  the  stars 
from  the  spectroscopic  point  of  view. 

383.  Secchi's  Classes  of  Spectra.  —  He  made  four  classes, 
as  follows: 

I.  Those  which  have  a  spectrum  characterized  by  great 
intensity     of 

the  dark  lines 
of  hydrogen, 
all  other  lines 
being  compara- 
tively feeble  or 
absent.  This 
class  comprises 
more  than  half 
of  all  the  stars, 
—  nearly  all 
the  stars  which 
are  white  or 
of  a  bluish  tinge.  Sirius  and  Vega  are  its  types. 

II.  Those  which  show  a  spectrum  resembling  that  of  the 
sun ;  i.e.,  marked  with  a  great  number  of  fine  dark  lines. 
Capella  (Alpha  Aurigse)  and  Pollux  (Beta  Geminorum) 
are   conspicuous   examples.     The   stars   of  this   class  are 
also   numerous.     The   first   and   second   classes    together 
comprise  fully  seven-eighths  of  all  the  stars  whose  spectra 
are  known. 


FIG.  86.  —  Secchi's  Types  of  Stellar  Spectra 
Keeler 


322  LESSONS  IN  ASTRONOMY 

Certain  stars,  like  Procyon  and  Altair,  seem  to  be  intermediate 
between  the  first  and  second  classes,  and  help  us  to  trace  the 
probable  order  of  evolution. 

III.  Stars  which  show  a  spectrum  characterized  by  dark 
bands,  sharply  defined  at  the  upper  or  more  refrangible  edge 
and  shading  out  towards  the  red.     Most  of  the  red  stars 
and  a  large  number  of  the  variable  stars  belong  to  this 
class.    Some  of  them  show  also  bright  lines  in  their  spectra. 

IV.  This  class  comprises  only  a  few  small  stars,  which, 
like  the  preceding,  show  dark  bands,  but  shading  in  the 
opposite  direction.     Usually  they  also  show  a  few  bright 
lines.     There  are  not  a  few  anomalous  stars  that  will  not 
fall  into  any  of  these  classes. 

This  classification  is  the  basis  of  the  Harvard  system  now  very 
generally  used  for  detailed  study.  Different  types  are  indicated  by 
letters,  arranged  so  as  to  show  a  possible  order  of  evolution  based 
upon  increasing  complexity  of  spectrum.  Secchi's  Type  I  is  sub- 
divided into  Harvard  Types  B  and  A,  II  into  F,  G,  K,  while  III 
corresponds  to  M,  IV  to  N. 

364.  Photography  of  Stellar  Spectra.  —  The  observation 
of  these  spectra  by  the  eye  is  very  tedious  and  difficult,  and 
photography  comes  in  most  effectively.  Huggins  in  Eng- 
land and  Henry  Draper  in  this  country  were  the  pioneers, 
and  fine  results  in  this  line  have  been  obtained  by  E.  C. 
Pickering,  of  Cambridge,  in  connection  with  the  Draper 
Memorial  Fund.  Most  observers  use  the  prismatic  spectro- 
scope with  a  slit,  photographing  the  spectra  of  stars  one  by 
one,  and  having  for  comparison  the  spectra  of  known  metals 
upon  the  same  plate.  Pickering  has  recurred  to  the  old 
method  of  Fraunhofer,  using  a  prism  or  prisms  in  front  of 
the  object-glass  of  his  photographic  telescope,  thus  forming  a 


PHOTOGRAPHY  OF  STAR  SPECTRA  323 

44  slitless  spectroscope."  The  edges  of  the  prism  or  prisms 
are  placed  east  and  west.  If  the  clockwork  of  the  instru- 
ment followed  the  star  exactly,  the  spectrum  formed  on 
the  sensitive  plate  would  be  a  mere  narrow  streak ;  but  by 
allowing  the  clock  to  gain  or  lose  slightly,  the  image  of  the 
star  will  move  to  the  east  or  west  by  a  very  small  quantity 
during  the  exposure,  converting  the  streak  into  a  band. 

The  slitless  spectroscope  has  three  great  advantages  :  (1)  it  saves 
all  the  light  which  comes  from  the  star,  much  of  which,  in  the  usual 


JSirius 


Procyon 


Capella 


FIG.  87.  — Star  Spectra 
Pickering 

form  of  the  instrument,  is  lost  in  the  jaws  of  the  slit ;  (2)  by  taking 
advantage  of  the  length  of  a  large  telescope,  it  produces  a  long  spec- 
trum with  even  a  single  prism  ;  (3)  and  most  important  of  all, 
it  gives  on  the  same  plate  and  with  a  single  exposure  the  spectra  of  all 
the  many  stars  (sometimes  more  than  a  hundred)  whose  images  fall  upon 
the  plate. 

On  the  other  hand,  the  giving  up  of  the  slit  precludes  the  usual 
methods  of  identifying  the  lines  and  measuring  their  displacements 
by  actually  confronting  them  with  comparison  spectra.  For  instance, 
it  has  not  yet  been  found  possible  to  use  the  slitless  spectroscope  for 
determining  the  radical  velocities  of  stars,  i.e.,  their  absolute  rates 
of  approach  or  recession  (Sec.  341). 


324  LESSONS  IN  ASTRONOMY 

364*.  With  the  eleven-inch  telescope  formerly  belong- 
ing to  Dr.  Draper,  and  a  battery  of  four  enormous  prisms 
placed  in  front  of  the  object-glass,  spectra  are  obtained 
with  an  exposure  of  thirty  minutes,  which,  before  enlarge- 
ment, are  fully  three  inches  long  from  the  F  line  to  the 
ultra-violet  extremity.  They  easily  bear  tenfold  enlarge- 
ment and  show  many  hundreds  of  lines  in  the  spectra  of 
the  stars  which  belong  to  Secchi's  second  class.  Fig.  87 
shows  the  blue  and  violet  portion  of  the  spectra  of  Sirius, 
Procyon,  and  Capella  as  thus  photographed,  and  brings 
out  clearly  the  gradual  transition  between  stars  of  the  first 
and  second  classes.  The  photographs  fail  to  show  the 
lower  portion  of  the  spectrum,  i.e.,  the  red,  yellow,  and 
green  ;  but  within  a  few  years  the  use  of  isochromatic 
plates  has  made  it  possible  to  deal  with  these  colors  also. 

The  spectra  of  all  the  naked-eye  stars  in  both  of  the 
hemispheres  have  already  been  photographed  and  cata- 
logued, and  the  classification  of  about  214,000  stars,  which 
will  probably  extend  the  work  so  as  to  include  all  down  to 
the  ninth  magnitude,  will  be  given  in  the  New  Draper 
Catalogue,  prepared  by  Miss  Cannon  of  the  Harvard 
College  Observatory. 

Photography  of  stellar  spectra  is  now  a  part  of  the 
regular  program  of  nearly  all  large  observatories,  and  its 
importance  is  shown  by  the  fact  that  from  the  spectrum 
of  a  star  we  may  tell  with  some  certainty  the  speed  with 
which  the  star  is  moving  toward  or  away  from  the  earth, 
the  stage  of  physical  development  it  has  reached,  and  even, 
in  some  cases,  its  order  of  distance  from  us. 

365.  Twinkling,  or  Scintillation,  of  the  Stars.  —  This  phenomenon 
is  purely  physical,  and  not  in  the  least  astronomical.  It  depends 


SCINTILLATION  OF  THE  STARS  325 

both  upon  the  irregularities  of  refraction  in  the  air  traversed  by  the 
light  on  its  way  to  the  eye  (due  to  winds  and  differences  of  tempera- 
ture), and  also  on  the  fact  that  a  star  is  optically  a  luminous  point 
without  apparent  size,  —  a  fact  which,  under  the  circumstances,  gives 
rise  to  the  optical  phenomenon  known  as  interference.  Planets  which 
have  disks  measurable  with  a  micrometer  do  not  sensibly  twinkle. 

The  scintillation  is  of  course  greatest  near  the  horizon,  and  on 
a  good  night  it  practically  disappears  at  the  zenith.  When  the 
image  of  a  twinkling  star  is  examined  with  the  spectroscope,  dark 
interference  bands  are  seen  moving  back  and  forth  in  its  spectrum. 

NOTE  TO  ARTICLE  361 

Since  1902  several  limited  areas  in  the  heavens  have  been  discov- 
ered abnormally  rich  in  variable  stars,  —  tracts  only  a  few  degrees 
square,  in  which  variables  are  found  by  scores  upon  the  photographic 
negatives.  The  most  notable  are  one  discovered  by  Wolf  in  the  con- 
stellation of  Aquila,  and  those  discovered  by  the  Harvard  observers 
around  the  great  nebula  of  Orion,  in  Scorpio  and  Sagittarius,  and  in 
the  two  "  Magellanic  clouds  "  near  the  south  pole.  Obviously  they 
indicate  regions  of  space  where  conditions  differ  from  those  that 
generally  prevail,  —  a  peculiar  stage  of  cosmic  evolution. 

Professor  Pickering  in  his  observatory  report,  dated  Sept.  30, 1905, 
states  that  since  the  Harvard  photographic  work  began  in  1886, 
2750  variables  have  been  discovered,  —  about  555  elsewhere  and 
2197  at  Cambridge.  Mrs.  Fleming  has  discovered  8  "novae"  and 
197  variables,  mainly  by  bright  hydrogen  lines  in  their  spectra; 
Professor  Bailey  has  detected  509  in  globular  star-clusters  ;  and 
Miss  Leavitt  1442,  mostly  in  and  near  the  Magellanic  clouds.  And 
since  that  time  the  list  has  been  considerably  lengthened. 

Of  course  nearly  all  of  these  new  variables  are  extremely  faint,  ob- 
servable only  by  great  telescopes  or  by  photography ;  and  for  the  great 
majority  nothing  is  yet  known  as  to  the  period  and  type  of  variation. 

The  total  number  of  variables  which  can  be  reached  by  our  pres- 
ent instruments  must  be  hundreds  of  thousands,  and  not  improbably 
millions.  Among  the  6000  naked-eye  stars  about  70  variables  are 
already  known,  and  there  is  no  reason  to  suppose  that  the  proportion 
is  different  for  the  telescopic  stars. 


CHAPTER   XII 

THE  STARS  (Continued) 

Double  and  Multiple  Stars  and  Clusters  —  Nebulae  —  Distribution  of  Stars 
and  Constitution  of  the  Stellar  Universe  —  Cosmogony  and  the  Nebular 
Hypothesis 

366.  Double  Stars.  —  The  telescope  shows  numerous 
cases  in  which  two  .stars  lie  so  near  each  other  that  they 
can  be  separated  only  by  a  high  magnifying  power.  These 
are  double  stars  and  at  present  at  least  16,000  such 
couples  are  known.  There  is  also  a  considerable  number 
of  triple  stars  and  a  few  which  are  quadruple.  Fig.  88 
represents  a  few  of  the  best  known  objects  of  each  class. 
The  apparent  distances  generally  range  from  30"  down- 
wards, very  few  telescopes  being  able  to  separate  stars 
closer  than  a  quarter  of  a  second. 

In  a  large  proportion  of  cases  (perhaps  a  third  of  all), 
the  two  components  are  nearly  equal  in  brightness ;  but 
in  many  they  are  very  unequal :  in  that  case  (never  when 
they  are  equal),  they  often  present  contrasts  of  color,  and 
when  they  do  the  smaller  star  (for  some  reason  not  known) 
always,  or  with  very  few  and  doubtful  exceptions,  has  a 
tint  higher  in  the  spectrum  than  that  of  the  larger,  —  if  the 
larger  is  reddish  or  yellow,  the  small  star  will  be  green, 
blue,  or  purple. 

Gamma  Andromedae  and  Beta  Cygni  are  fine  examples  of  colored 
doubles  for  a  small  telescope. 


OPTICAL  AND  PHYSICAL  DOUBLES  327 

367.  Stars  optically  and  physically  Double.  —  Stars  may 
be  double  in  two  ways,  —  optically  or  physically.  In  the 
first  case  they  are  only  approximately  in  line  with  each 
other  as  seen  from  the  earth ;  in  the  second  case,  they  are 
really  near  each  other.  In  the  case  of  stars  that  are  only 
optically  double  it  usually  happens  that  after  some  years 


FIG.  88.  —  Double  and  Multiple  Stars 

we  can  detect  their  mutual  independence  by  the  fact  that 
their  relative  motion  is  in  a  straight  line  and  uniform,  i.e., 
one  of  them  drifts  by  the  other  in  a  line  which  is  perfectly 
straight.  TJiis  is  a  simple  consequence  of  the  combina- 
tion of  their  independent  "  proper  motions."  If  they  are 
physically  connected,  we  find,  on  the  contrary,  that  the  rel- 
ative motion  is  hi  a  concave  curve;  i.e.,  taking  either  of 


328  LESSONS  IN  ASTRONOMY 

them  as  a  center,  the  other  one  appears  to  move  around 
it  in  a  curve. 

The  doctrine  of  chances  shows,  what  direct  observation 
confirms,  that  optical  pairs  must  be  comparatively  rare 
and  that  the  great  majority  of  double  stars  must  be  really 
physically  connected, — probably  by  the  same  attraction  of 
gravitation  which  controls  the  solar  system. 

368,  Binary  Stars.  —  Stars  thus  physically  connected 
are  also  known  as  "  binary  "  stars.  They  revolve  in  ellip- 
tical orbits  around  their  common  center  of  gravity  in 
periods  which  range  from  14  years  to  1500  (so  far  as  at 
present  known),  while  the  apparent  length  of  the  ovals 
ranges  from  0".4  to  40".  The  elder  Herschel,  a  little 
more  than  a  century  ago,  first  discovered  this  orbital 
motion  of  "  binaries  "  in  trying  to  ascertain  the  parallax 
of  some  of  the  few  double  stars  which  were  known  at 
his  time.  It  was  then  supposed  that  they  were  simply 
optical  pairs,  and  he  expected  to  detect  an  annual  dis- 
placement of  one  member  of  the  pair  with  reference  to 
the  other,  from  which  he  could  infer  its  annual  parallax 
(Sec.  343).  He  failed  in  this,  but  found  instead  a  true 
orbital  motion. 

The  apparent  orbit  is  always  an  ellipse ;  but  this  appar- 
ent orbit  is  the  true  orbit  seen  more  or  less  obliquely,  so 
that  the  larger  star  is  not  usually  in  the  focus  of  the 
relative  orbit  pursued  by  the  smaller  one.  II  we  assume 
what  is  probable  (though  certainly  not  proved  as  yet),  that 
the  orbital  motion  of  the  pair  is  under  the  law  of  gravita- 
tion, we  know  that  the  larger  star  must  be  in  the  focus 
of  the  true  relative  orbit  of  the  smaller,  and,  moreover, 
that  the  latter  must  describe  around  it  equal  areas  in  equal 


ORBITS  OF  BINARY  STARS 


329 


times.  By  the  help  of  these  principles  we  can,  if  we  have 
observations  sufficiently  numerous  and  accurate,  deduce 
from  the  apparent  oval  the  true  orbital  ellipse;  but  the 
calculation  is  troublesome  and  delicate. 

369.  At  present  the  number  of   pairs  in  which  this  kind  of 
motion   has   been   certainly  detected  exceeds  200,   and   it  is  con- 
tinually increasing  as  our  study  of  the  double  stars  goes  on.     About 
fifty  pairs  have  progressed  so  far,  either  having  completed  an  entire 
revolution  or  a  large  part  of  one,  that  it  is  possible  to  determine 
their  orbits  with  some  accuracy. 

The  case  of  Sirius  is  peculiar.  As  long  ago  as  1844  it  had  been 
found  from  meridian-circle  observations  to  be  moving,  for  no  then 
assignable  reason,  in  a 
small  orbit  with  a  period 
of  about  fifty  years.  In 
1862  Alvan  G.  Clark,  a 
member  of  the  famous 
Cambridgeport  firm  of 
telescope  makers,  found 
near  it  a  minute  compan- 
ion, which  explains  every- 
thing ;  only  we  have  to 
admit  that  this  faint 
attendant,  which  does  not 

give  a  ten-thousandth  as  much  light  as  Sirius  itself,  has  a  mass 
nearly  two-fifths  as  great.  It  seems  to  be  one  of  Bessel's  dark  stars. 
Fig.  89  represents  the  apparent  orbits  of  two  of  the  best  determined 
double-star  systems,  Gamma  Virginis  and  Xi  Ursse  Majoris. 

370.  Size  and  Form  of  the  Orbits.  —  The  dimensions  of 
a  double-star  orbit  can  easily  be  obtained  if  we  know  its 
distance  from  us.     Fortunately,  a  number  of  stars  whose 
parallaxes    have   been    ascertained   are    also   binary,  and 
assuming  the  best  available  data,  we  have  the  results  given 
in  the  little  table  which  follows,  —  the  real  semi-major 


1 

186^- \ 

61  Years  V856 
2/1821 


1718 
7  Virginis 


90° 


I0o 

Ursce  Majoris 


FIG.  89.  —  Orbits  of  Binary  Stars 


330 


LESSONS  IN  ASTRONOMY 


axis  of  the  orbit  (in  astronomical  units)  being  always  equal 

a" 
to  the  fraction  — »  in  which  a"  is  the  angular  semi-major 

axis  of  the  real  (not  apparent)  orbit  in  seconds  of  arc,  and 
pn  the  parallax  of  the  star.  But  it  must  not  be  forgotten 
that  there  is  still  considerable  uncertainty  in  the  data, 
especially  in  the  parallaxes. 


NAME 

ASSUMED 
PARALLAX 

ANGULAR 
SEMI-AXIS 

REAL, 

SEMI-AXIS 

PERIOD 

MASS 
0  =  1 

Eta  Cassiopeia^  .  . 
Sirius  ....... 

0".35 
0.39 

8".  21 
8.03 

23.5 
20.6 

195y.8 

52.2 

0.33 
3.24 

Alpha  Centauri  .  . 
70  Ophiuchi  .... 

0.75 
0.16 

17.70 
4.54 

23.6 
30.3 

81.1 

88.4 

2.00 
3.56 

These  double-star  orbits  are  evidently  comparable  in 
magnitude  with  the  larger  orbits  of  the  planetary  system, 
none  of  those  given  being  smaller  than  the  orbit  of  Uranus 
and  none  much  larger  than  that  of  Neptune.  In  form 
they  are  much  more  eccentric  than  planetary  orbits,  and 
it  has  been  shown  that  this  fact  can  be  accounted  for 
as  a  result  of  "tidal  evolution,"  operating  upon  a  pair 
of  nebulous  masses,  formed  by  the  separation  of  a  parent 
nebula  into  two  portions  which  revolve  around  their 
common  center. 

371.  Masses  of  Binary  Stars.  —  If  we  assume  that  the 
binary  stars  move  under  the  law  of  gravitation,  then,  when 
we  know  the  semi-major  axis  of  the  orbit  and  the  period 
of  revolution,  we  can  easily  find  the  mass  of  the  pair  as 
compared  with  that  of  the  sun,  much  more  easily,  indeed, 
than  we  can  determine  the  'mass  of  Mercury  or  the 
moon,  strange  as  it  may  seem.  It  is  done  simply  by  the 


MASSES  OF  BINARY  STARS  331 

following  equation,  which  we  give  without  demonstration 
(see  General  Astronomy,  Arts.  536  and  878): 


in  which  (M  +  m)  is  the  united  mass  of  the  two  stars,  S  is 
the  mass  of  the  sun,  a  is  the  semi  -major  axis  of  the  orbit 
of  the  double  star  in  astronomical  units,  and  t  its  period  in 
years.  The  final  column  of  the  preceding  table  gives  the 
masses  of  the  star  pairs  resulting  from  the  data  given  in 
the  table  ;  but  the  reader  must  bear  in  mind  that  the 
margin  of  error  is  very  considerable  because  of  the  uncer- 
tainty of  the  orbits  and  parallaxes  in  question.  A  very 
slight  error  in  the  parallax  makes  a  very  great  error  in  the 
resulting  mass. 

372.  Planetary  Systems  attending  Stars.  —  It  is  a  natural  ques- 
tion whether  some  of  the  small  companions  which  we  see  near  large 
stars  may  not  be  the  "  Jupiters  "  of  their  planetary  systems.     We  can 
only  say  as  to  this  that  no  telescope  ever  constructed  could  even  come 
near  to  making  visible  a  planet  which  bears  to  its  primary  any  such 
relations  of  size,  distance,  and  brightness  as  Jupiter  bears  to  the  sun. 
Viewed  from  our  nearest  neighbor  among  the  stars,  Jupiter  would  be 
a  little  star  of  about  the  twenty-first  magnitude,  not  quite  5"  distance 
from  the  sun,  which  itself  would  look  like  a  star  of  the  second  mag- 
nitude.    To  render  a  star  of  the  twenty-first  magnitude  barely  visible 
(apart  from  all  the  difficulties  raised  by  the  nearness  of  a  larger  star) 
would  require  a  telescope  more  than  twenty  feet  in  diameter.     If  any 
of  the  stars  have  planetary  systems  accompanying  them,  we  shall 
never  be  likely  to  see  them  until  our  telescopes  have  attained  a 
magnitude  and  power  as  yet  undreamed  of. 

373.  Spectroscopic  Binaries.  —  One  of  the  most  interest- 
ing of  recent  astronomical  results  is  the  detection  by  the 
spectroscope  of  many  pairs  of  double  stars  so  close  that  no 


332  LESSONS  IN  ASTRONOMY 

telescope  can  separate  them.  In  1889  the  bright  com- 
ponent of  the  well-known  double  star  Mizar  (Zeta  Ursse 
Majoris,  Fig.  88)  was  found  by  Pickering  to  show  the  dark 
lines  double  in  the  photographs  of  its  spectrum,  at  regular 
intervals  of  about  fifty-two  days.  The  obvious  explana- 
tion is  that  this  star  is  composed  of  two,  which  revolve 
around  their  common  center  of  gravity  in  an  orbit  which 
is  turned  nearly  edgewise  toward  us.  (If  it  was  exactly 
edgewise,  the  star  would  be  variable  like  Algol.) 

When  the  stars  are  at  right  angles  to  the  line  from  them 
to  us,  one  of  the  two  will  be  moving  towards  us,  while  the 
other  is  moving  in  an  opposite  direction  ;  and  as  a  con- 
sequence, the  lines  in  their  spectra  will  be  shifted  opposite 
ways,  according  to  Doppler's  principle  (Sec.  179).  Now 
since  the  two  stars  are  so  close  that  their  spectra  overlie 
each  other,  the  result  will  be  simply  to  make  the  lines  in 
the  compound  spectrum  look  double.  From  the  distance 
apart  of  the  lines  the  relative  velocity  of  the  stars  can  be 
found,  and  from  this  the  size  of  the  orbit  and  the  mass  of 
the  stars.  Pickering  inferred  from  his  observations  that 
in  the  case  of  Mizar  the  relative  velocity  of  the  two  com- 
ponents is  about  100  miles  per  second,  the  period  about 
104  days,  and  the  distance  between  the  two  stars  about  the 
same  as  the  diameter  of  the  orbit  of  Mars.  Later  observa- 
tions by  Vogel,  while  confirming  the  velocity  observed  by 
Pickering,  have  shown  that  the  period  is  only  20.6  days, 
—  just  one-fifth  of  Pickering's  value,  making  the  orbit 
smaller  than  that  of  Mercury. 

Mizar  is  really  a  quadruple  star,  both  of  the  two  which  are  seen 
in  a  small  telescope  being  spectroscopically  double. 


SPECTROSCOPIC  BINARIES  333 

The  lines  in  the  spectrum  of  Beta  Aurigse  exhibit  the 
same  peculiarity,  but  the  doubling  occurs  once  in  four 
days,  —  the  velocity  being  about  150  miles  a  second  and 
the  diameter  of  the  orbit  about  8,000000  miles,  while  the 
united  mass  of  the  two  stars  is  about  two  and  a  half  times 
that  of  the  sun. 

These  observations  of  Professor  Pickering's  were  made 
by  photographing  the  spectrum  with  the  slitless  spectro- 
scope (Sec.  364),  and  are  possible  only  where  the  stars 
which  compose  the  binary  are  both  of  them  reasonably 
bright. 

374.  With  his  slit-spectroscope,  Vogel  (Sec.  341),  as  has 
already  been  stated  (Sec.  360),  has  been  able  to  detect  a 
similar  orbital  motion  in  Algol,  although  the  companion 
of  the  brighter  star  is  itself  invisible.  A  little  later,  in  the 
case  of  the  bright  star  Alpha  Virginis  (Spica),  he  found 
a  result  of  the  same  kind.  At  first  the  photographic 
observations  of  the  spectrum  of  this  star  appeared  very 
discordant.  Some  days  they  indicated  that  the  star  was 
moving  towards  us  quite  rapidly,  and  then  again  from 
us ;  but  it  is  found  that  everything  can  be  explained  by 
the  simple  supposition  that  the  star  is  double,  with  a  small 
companion  like  that  of  Algol,  not  bright  enough  to  show 
itself  by  its  light,  but  heavy  enough  to  make  its  partner 
swing  around  in  an  orbit  about  6,000000  miles  in  diameter 
once  in  four  days,  —  the  orbit  not  being  quite  edgewise  to 
the  earth,  so  that  the  dark  companion  does  not  eclipse 
Spica  as  Algol  is  eclipsed  by  its  attendant.  Many  such 
systems  are  found,  in  which  the  presence  of  a  darker  com- 
panion is  made  known  only  by  the  variable  radial  velocity 
of  the  brighter  star. 


334  LESSONS  IN  ASTRONOMY 

The  most  remarkable  spectroscopic  binaries  thus  far  detected  are, 
however,  two  which  were  discovered  in  1896  by  spectrum  photographs 
made  at  Arequipa.  The  first  is  Mu1  Scorpii,  in  which  the  relative 
velocity  of  the  components  is  nearly  300  miles  a  second.  The  other 
is  a  little  star  of  the  fifth  magnitude,  known  as  "  Lacaille  3105,"  in 
which  the  relative  velocity  of  the  two  stars  is  385  miles  a  second  (!), 
and  since  the  period  is  74£  hours,  the  mass  must  be  about  77  times 
that  of  the  sun. 

At  present  more  than  three  hundred  objects  of  this  sort  are  known, 
among  them  Capella  and  the  Pole-star,  the  latter  having  a  period  of 
3d23h,  and  an  apparent  relative  velocity  of  only  four  miles  a  second. 
The  catalogue  of  such  objects  is  growing  rapidly. 

375.  Multiple  Stars  (see  Fig.  88).  —  In  a  considerable 
number  of  cases  we  find  three  or  more  stars  connected  in 
one  system.  Zeta  Cancri  consists  of  a  close  pair  revolving 
in  a  nearly  circular  orbit,  with  a  period  somewhat  less  than 
sixty  years,  while  a  third  star  revolves  in  the  same  direc- 
tion around  them  at  a  much  greater  distance  and  with  a 
period  not  less  than  500  years  (not  yet  fully  determined). 
Moreover,  this  third  star  is  subject  to  a  peculiar  irregularity 
in  its  motion,  which  seems  to  indicate  that  it  has  an  invisible 
companion  very  near  the  system,  the  system  being  really 
quadruple. 

In  Epsilon  Lyrse  we  have  a  beautiful  quadruple  system, 
composed  of  two  pairs,  each  binary  with  a  period  of  over 
200  years.  Moreover,  since  they  have  a  common  proper 
motion,  it  is  probable  that  the  two  pairs  revolve  around 
each  other  in  a  period  which  can  be  reckoned  only  in 
thousands  of  years. 

In  Theta  Orionis  we  have  a  remarkable  object  in  which 
the  six  components  are  not  organized  in  pairs,  but  are  at 
not  very  unequal  distances  from  each  other. 


STAR-CLUSTERS 


335 


Asterope 


376.  Clusters.  —  There  are  in  the  sky  numerous  groups 
of  stars,  containing  from  a  hundred  to  many  thousand 
members.  A  few  of  them  are  resolvable  by  the  naked  eye, 
as,  for  instance,  the  Pleiades  (Fig.  90) ;  some,  like  Prsesepe 
in  Cancer,  break  up  under  the  power  of  even  an  opera- 
glass  (Sec.  52) ;  but  most  of  them  require  a  large  telescope 
to  show  the  separate  components.  To  the  naked  eye  or 
small  telescopes,  if 
visible  at  all,  they 
look  like  faint 
clouds  of  shining 
haze,  but  in  a  great 
telescope  they  are 
among  the  most 
magnificent  objects 
the  heavens  afford. 
The  cluster  known 
as  "13  Messier," 
in  the  constellation 
of  Hercules,  is  one 
of  the  finest. 

The  question  at 
once  arises  whether  FlG' 90—  MaP  of  the  pleiades 

the  stars  in  such  a  cluster  are  comparable  with  our  own  sun 
in  magnitude  and  separated  from  each  other  by  distances 
like  that  between  the  sun  and  Alpha  Centauri,  or  whether 
they  are  really  small  (for  stars)  and  closely  packed ;  whether 
the  swarm  is  no  more  distant  than  the  rest  of  the  stars  or 
far  beyond  them. 

The  Hercules   cluster   contains   at   least    30,000    stars 
packed  within  an  area  less  than  10'  in  diameter.     While 


PZeione* 
Atlas? 


336  LESSONS  IN  ASTRONOMY 

the  evidence  may  not  be  conclusive,  recent  investigations 
seem  to  indicate  that  this  cluster  may  be  as  distant  as 
100,000  light-years.  If  that  be  so,  individual  stars  must 
be  more  luminous  than  our  sun,  it  may  take  1000  years 
for  light  to  travel  from  one  side  to  the  other,  and  the 
actual  distances  between  members  of  the  cluster  must  be 
enormous,  though  perhaps  less  than  that  which  separates 
our  sun  from  its  nearest  neighbor. 

NEBULAE 

377.  Besides  the  luminous  clouds  which,  under  the  tele- 
scope, break  up  into  separate  stars,  there  are  others  which 
no  telescopic  power  resolves,  and  among  them  some  which 
are  brighter  than  many  of  the  clusters.  These  irresolvable 
objects,  of  which  about  10,000  are  now  catalogued,  with 
probably  myriads  more  not  yet  entered  on  the  list,  are 
"  nebulae."  Two  or  three  of  them  are  visible  to  the  naked 
eye,  —  one,  the  brightest  of  all  and  the  one  in  which  the 
temporary  star  of  1885  appeared,  is  in  the  constellation  of 
Andromeda  (see  Fig.  91).  Another  most  conspicuous  and 
very  beautiful  nebula  is  that  in  the  sword  of  Orion. 

The  larger  and  brighter  nebulae  are,  for  the  most  part, 
irregular  in  form,  sending  out  sprays  and  streams  in  all 
directions  and  containing  dark  openings  and  "lanes." 
Some  of  them  are  of  enormous  volume.  The  great  nebula 
of  Orion  (which  includes  within  its  boundary  the  mul- 
tiple star  Theta  Orionis)  covers  several  square  degrees, 
and  photographs  show  that  nearly  the  whole  constellation 
is  enveloped  in  a  faint  nebulosity,  the  wisps  attaching 
themselves  especially  to  the  brighter  stars. 


THE  NEBULAE  337 

The  nebula  of  Andromeda  is  not  quite  so  extensive,  but 
is  more  regular  in  its  form,  —  a  long  oval  with  dark  lanes 
in  it,  and  a  bright  nucleus  much  like  a  star  in  the  center, 
as  seen  in  a  small  telescope. 

The  smaller  nebulae  are,  for  the  most  part,  more  or  less 
nearly  oval  and  brighter  in  the  center.  In  the  so-called 


FIG.  91.  —  Nebula  in  Audromeda 
Roberts 


"  nebulous  stars  "  the  central  nucleus  is  like  a  star  shining 
through  a  fog.  The  "  planetary  nebulae  "  are  about  circular 
and  have  a  nearly  uniform  brightness  throughout,  while 
the  rare  " annular"  or  "ring  nebulae"  are  darker  in  the 
center.  Fig.  92  is  from  a  photograph  of  the  finest  of  these 
ring  nebulae,  that  in  the  constellation  of  Lyra.  There 


338 


LESSONS  IN  ASTRONOMY 


are  a  number  of  nebulae  which  exhibit  a  remarkable 
spiral  structure  in  large  telescopes.  There  are  several 
double  nebulae  and  a  few  that  are  variable  in  brightness, 
though  no  regularity  has  yet  been  ascertained  in  their 
variation.  Many  of  the  most  conspicuous  and  interest- 
ing are,  how- 
ever, extremely 
irregular  in 
form  and  struc- 
ture, as  for  In- 
stance, the  Tri- 
fid  Nebula  and 
the  great  nebula 
of  Orion  (Figs. 
93  and  94). 

The  great 
majority  of  the 
nebulae  are  ex- 
tremely faint, 
even  in  large 
telescopes,  but 
the  few  that 
are  reasonably  bright  are  very  interesting  objects. 

378.  Drawings  and  Photographs  of  Nebulae.  —  Until  very 
lately  the  correct  representation  of  a  nebula  was  an  extremely 
difficult  task.  More  or  less  elaborate  engravings  exist  of 
perhaps  fifty  of  the  more  conspicuous  of  them,  but  pho- 
tography has  now  taken  possession  of  the  field.  The  first 
success  in  this  line  was  by  Henry  Draper  of  New  York,  in 
1880,  in  photographing  the  nebula  of  Orion.  Since  his 
death  in  1882  great  progress  has  been  made,  both  in  Europe 


FIG.  92.  —  Annular  Nebula  in  Lyra 
Keeler 


FIG.  93.  —  Trifid  Nebula 
Keeler 


FIG.  94.  —  Great  Nebula  in  Orion 
Keeler 

339 


340 


LESSONS  IN  ASTRONOMY 


and  in  this  country,  and  at  present  the  photographs  are 
continually  bringing  out  new  and  before  unsuspected 
features.  Fig.  91,  for  instance,  from  a  photograph  of  the 
nebula  of  Andromeda,  taken  by  Mr.  Roberts  of  Liverpool 

in  1 8  8  8,  shows  that 
the  so-called  "  dark 
lanes,"  which  hith- 
erto had  been  seen 
only  as  straight 
and  wholly  myste- 
rious  markings, 
are  really  curved 
ovals,  like  the  di- 
visions in  Saturn's 
rings.  The  photo- 
graph brings  out 
clearly  a  distinct 
spiral  structure 
pervading  the 
whole  nebula, 
which  as  yet  has 
aever  been  made  out  satisfactorily  by  the  eye  with  any 
telescope.  This  spiral  structure  is  found  more  or  less  evi- 
dent in  a  great  majority  of  the  nebulae.  Fig.  95,  the  so- 
called  "whirlpool  nebula"  in  the  constellation  of  Canes 
Venatici,  is  its  finest  example. 

The  photographs  not  only  show  new  features  in  old  nebulae,  but 
they  reveal  numbers  of  new  nebulae  invisible  to  the  eye  with  any  tele- 
scope. Thus,  in  the  Pleiades,  it  has  been  found  that  almost  all  the 
larger  stars  have  wisps  of  nebulosity  attached  to  them,  as  indicated 
by  the  dotted  lines  in  Fig.  90,  and  shown  fully  developed  in  the 


Fia.  95.  —  Spiral  Nebula 
Keeler 


CHANGES  IN  NEBULA 


341 


photograph  of  Fig.  96 ;  and  in  a  small  territory  in  and  near  the 
constellation  of  Orion,  Pickering,  with  an  eight-inch  telescope,  found 
upon  his  star  plates  nearly  as  large  a  number  of  new  nebulae  as  of 
those  that  were  previously  known  within  the  same  boundary. 

The  photographs  of  nebulae  require  generally  an  exposure  of  from 
one  to  two  hours.  The  images  of  all  the  brighter  stars  that  fall  upon 
the  plate  are,  therefore,  always  immensely  overexposed,  and  seriously 
injure  the  picture  from  an  artistic  point  of  view. 

The  photographic  brightness  of  a  nebula,  to  use  such  an  expres- 
sion, is  many  times  greater  than  its  brightness  to  the  eye,  owing  to 
the  fact  that  its  light  consists  mainly  in  rays  which  belong  to  the 
upper  or  blue  portion  of  the  spectrum.  It  has  very  little  red  or 
yellow  in  it.  At  least, 
this  is  so  with  all  the 
nebulae  whose  spectra  are 
characterized  by  bright 
lines. 

379,  Changes    in 
Nebulae.  —  It  cannot  be 
stated  with  certainty  that 
sensible    changes     have 
occurred  in  any  of  the 
nebulae   since   they  first 
began  to  be  observed,  — 
the  early  instruments 
were  so  inferior  to  mod- 
ern ones  that  the  older 
drawings   cannot  be 
trusted ;  but  some  of  the 
differences  between  the 
older   and   more    recent 
representations  make  it 

extremely  likely  that  real  changes  are  going  on.  Probably  after 
a  reasonable  interval  of  time  photography  will  settle  the  question. 

380.  Spectra  of  Nebulae.  —  One  of  the  most  important 
of  the  early  achievements  of  the  spectroscope  was  the  proof 


FIG.  96.  —The  Pleiades 
Roberts 


342  LESSONS  IN  ASTRONOMY 

that  the  light  of  the  irregular  nebulae  proceeds  mainly 
from  glowing  gas  of  low  density,  and  not  from  aggregations 
of  stars.  Huggins,  in  1864,  first  made  the  decisive  obser- 
vation by  finding  bright  lines  in  their  spectra.  Thus  far  the 
spectra  of  all  the  nebulae  that  show  lines  at  all  appear  to 
be  substantially  the  same.  Four  lines  are  usually  easily 
observed,  two  of  which  are  due  to  hydrogen  ;  but  the 
other  two,  which  are  brighter  than  the  hydrogen  lines,  are 
not  yet  identified. 

Fig.  97  shows  the  position  of  the  principal  lines  so  far  visually 
observed.  In  the  brighter  nebulae  a  number  of  others  are  also  some- 
times seen  and  photographs  show  nearly  one  hundred  in  all,  among 


FIG.  97.  —  Spectrum  of  the  Gaseous  Nebulae 

which  are  several  of  the  lines  of  helium.  Certain  stars  also  show  the 
nebular  lines  in  their  spectra,  and  Mr.  Campbell  has  found  one  or 
two  which  show  bright  hydrogen  lines  extending  out  on  each  side 
of  the  star  spectrum  in  such  a  way  as  to  indicate  an  immense 
envelope  of  the  gas  surrounding  the  star  itself.  From  the  displace- 
ment of  the  lines  of  their  spectra  it  has  been  found  that  the  irregu- 
lar nebulae  are  moving  very  slowly,  while  the  average  radial  velocity 
of  the  planetary  is  48  miles  a  second,  and  that  of  the  spiral  several 
times  as  great  as  the  planetary. 

381.  Not  all  nebulae  show  the  bright-line  spectrum. 
Those  which  do  (known  as  gaseous  nebulae)  are  of  a 
greenish  tint,  at  once  recognizable  in  a  large  telescope. 


DISTANCE  AND  DISTRIBUTION  OF  NEBULAE    343 

The  white  nebulae  are  probably  all  spiral  in  form.  Most 
of  them  are  intrinsically  too  faint  to  be  studied  with  the 
spectroscope,  but  the  brightest  ones  (including  the  great 
nebula  of  Andromeda)  are  found  to  present  a  spectrum 
similar  to  that  of  our  sun  —  a  bright  band  crossed  by  dark 
absorption  lines.  This  is  just  what  we  might  expect  from 
a  very  distant  cloud  of  stars,  and  has  led  to  the  suggestion 
that  the  spiral  nebulae  may  be  other  universes  so  far  beyond 
the  limits  of  our  own  galaxy  that  none  of  the  individual 
stars  can  be  distinguished. 

We  can,  however,  only  speculate  as  to  the  real  nature 
of  these  bodies.  That  they  are  very  different  from  the 
irregular  nebulae  is  shown  not  only  by  the  difference  in 
form  and  spectrum  but  also  by  their  remarkable  radial 
velocity.  The  average  motion  in  line  of  sight  for  more 
than  a  score  of  spirals  is  about  250  miles  a  second,  and 
occasionally  it  runs  up  to  600  miles. 

382.  Distance  and  Distribution  of  Nebulae Very  little 

is  positively  known  as  to  the  distance  of  nebulae,  and  the 
method  commonly  used  in  finding  the  parallax  of  a  star 
cannot  often  be  applied.  However,  photographs  for  this 
purpose  have  been  taken  with  the  60-inch  reflector  on 
Mount  Wilson,  and  the  measures  indicate  that  the  parallax 
of  the  nebula  in  Andromeda  is  about  0".004,  and  that  the 
ring  nebula  in  Lyra  is  equally  distant.  The  planetary 
nebulae  may  be  nearer,  for  the  average  parallax  for  six  was 
found  in  1918  to  be  0".018,  corresponding  to  a  distance 
of  about  180  light-years. 

Most  of  the  irregular  nebulae  are  in  the  Milky  Way, 
and  seem  to  be  so  closely  connected  with  faint  stars  in  the 
vicinity  as  to  leave  little  doubt  that  they  lie  at  the  same 


344  LESSONS  IN  ASTRONOMY 

order  of  distance  as  the  stars.  It  seems  probable  that 
apparently  vacant  spaces  found  in  some  parts  of  the  sky 
may  be  explained  as  due  to  the  presence  of  dark  nebulous 
clouds  obscuring  the  light  from  stars  which  lie  beyond. 
It  seems  certain  that  these  nebulae  are  within  the  bound- 
aries of  our  stellar  system,  but  there  is  great  uncertainty 
as  to  the  status  of  the  spirals.  These  may,  perhaps,  be 
very  distant  members  of  our  universe,  or,  as  has  been  sug- 
gested, they  may  find  their  place  in  the  space  beyond.  If 
the  distance  could  be  known  with  certainty,  much  light 
would  be  thrown  upon  the  question  of  their  constitution. 
As  to  the  distribution,  we  find  the  green,  or  gaseous, 
nebulas  confined  almost  entirely  to  the  Milky  Way,  while 
the  white,  or  non-gaseous,  are  most  numerous  in  the  region 
of  the  northern  galactic  pole. 

THE   SIDEREAL    HEAVENS 

383.  The  Galaxy,  or  Milky  Way.  —  This  is  a  luminous 
belt  of  irregular  width  and  outline  which  surrounds  the 
heavens  nearly  in  a  great  circle.  It  is  very  different  in 
brightness  in  different  parts,  and  is  marked  here  and  there 
by  dark  bars  and  patches  which  at  night  look  like  over- 
lying clouds.  For  about  a  third  of  its  length  (between 
Cygnus  and  Scorpio)  it  is  divided  into  two  roughly  par- 
allel streams.  The  telescope  shows  it  to  be  made  up  almost 
entirely  of  small  stars  from  the  eighth  magnitude  down; 
it  contains  also  numerous  star-clusters,  but  very  few  true 
nebulae. 

The  galaxy  intersects  the  ecliptic  at  two  opposite  points 
not  far  from  the  solstices  and  at  an  angle  of  nearly  60°,  the 


DISTRIBUTION  OF  STARS  IN  THE  HEAVENS     345 

north  "  galactic  pole  "  being,  according  to  Herschel,  in  the 
constellation  of  Coma  Berenices.    As  Herschel  remarks : 

The  «  galactic  plane  "  is  to  the  sidereal  universe  much  what  the 
plane  of  the  ecliptic  is  to  the  solar  system, —  a  plane  of  ultimate 
reference,  and  the  ground  plan  of  the  stellar  system. 

384,  Distribution  of  Stars  in  the  Heavens.  —  It  is  obvi- 
ous that  the  distribution  of  the  stars  is  not  even  approxi- 
mately uniform.  They  gather  everywhere  into  groups 
and  streams;  but,  besides  this,  the  examination  of  any 
of  the  great  star-catalogues  shows  that  the  average  num- 
ber to  a  square  degree  increases  rapidly  and  pretty  regu- 
larly from  the  galactic  pole  to  the  galaxy  itself,  where 
they  are  most  thickly  packed.  This  is  best  shown  by 
the  "  star-gauges "  of  the  elder  Herschel,  each  of  which 
consists  merely  in  an  enumeration  of  the  stars  visible  in 
a  single  field  of  view.  He  made  3400  of  these  gauges, 
and  his  son  followed  up  the  work  at  the  Cape  of  Good 
Hope  with  2300  more  in  the  south  circumpolar  regions. 
From  these  data  it  appears  that  near  the  pole  of  the 
galaxy  the  average  number  of  stars  in  a  single  field  of 
view  is  only  about  4 ;  at  45°  from  the  galaxy,  a  little  over 
10;  while  on  the  galactic  circle  itself  it  is  122. 

Herschel,  starting  from  the  unsound  assumption  that  the  stars  are 
all  of  about  the  same  size  and  brightness  and  separated  by  approxi- 
mately equal  distances,  drew  from  his  observations  numerous  unten- 
able conclusions  as  to  the  form  and  structure  of  the  "  galactic 
cluster,"  to  which  the  sun  was  supposed  to  belong,  —  theories  for 
a  time  widely  accepted  and  even  yet  more  or  less  current  in  popular 
text-books,  though  in  many  points  certainly  incorrect. 

But  although  the  apparent  brightness  of  the  stars  does 
not  depend  entirely,  or  even  mainly,  upon  their  distance, 


346  LESSONS  IN  ASTRONOMY 

it  is  certain  that,  as  a  class,  the  faint  stars  are  really  more 
remote,  as  well  as  smaller  and  darker  than  the  brighter 
ones.  We  may,  therefore,  safely  draw  a  few  inferences, 
which,  so  far  as  they  go,  in  the  main  agree  with  Herschel. 
385.  Structure  of  the  Stellar  Universe.  —  I.  The  great 
majority  of  the  stars  we  see  are  included  within  a  space 
having  roughly  the  form  of  a  rather  thin  flat  disk,  like  a 
watch,  with  a  diameter  eight  or  ten  times  as  great  as  its 
thickness,  our  sun  being  not  very  far  from  its  center. 

II.  Within  this  space  the  naked-eye  stars  are  dis- 
tributed with  some  uniformity,  but  not  without  a  tend- 
ency to  cluster,  as  shown  in  the  Pleiades.  The  smaller 
stars,  on  the  other  hand,  are  strongly  "gregarious"  and 
are  largely  gathered  into  groups  and  streams  which  have 
comparatively  vacant  spaces  between  them. 

III.  At  right  angles  to  the  galactic  plane  the  stars  are 
scattered  more  evenly  and  thinly  than  in  it,  and  we  find 
on  the  sides  of  the  disk  the  comparatively  starless  region 
of  the  nebulae. 

IV.  As  .to   the   Milky  Way  itself,   it   is   not   certain 
whether  the  stars  which  compose  it  form  a  sort  of  thin, 
flat,  continuous  sheet,  or  whether  they  are  arranged  in  a 
sort  of   ring  with  a  comparatively  empty  space  in  the 
middle,  where  the  sun  is  situated,  not  far  from  its  center. 

As  to  the  size  of  the  disklike  space  which  contains  most  of  the 
stars,  very  little  can  be  said  positively.  Its  diameter  is  probably  as 
great  as  20,000  or  30,000  light-years,  —  how  much  greater  it  may  be 
we  cannot  even  guess,  and  as  to  the  "beyond"  we  are  still  more 
ignorant.  It  is  possible  that  our  galaxy,  as  seen  from  a  great  dis- 
tance, would  appear  like  a  spiral  nebula,  the  dark  rifts  being  the 
spaces  between  the  arms  of  the  spiral. 


QUESTION"  OF  A  STELLAR  SYSTEM  347 

386.  Do  the  Stars   form  a   System?  —  It   is   probable 
(though  not   certain)   that  gravitation    operates   between 
the  stars,  as  indicated  by  the  motion  of  the  binaries.     The 
stars  are  certainly  moving  very  swiftly  in  various  direc- 
tions,   and   the    question   is  whether   these    motions    are 
governed  by  gravitation,  and  are  "  orbital "  in  the  ordinary 
sense  of  the  word. 

There  has  been  a  very  persistent  belief  that  somewhere 
there  is  an  enormous  central  sun,  around  which  the  stars 
are  all  circulating  in  the  same  way  as  the  planets  of  the 
solar  system  move  about  our  own  sun.  This  belief  has 
been  abundantly  proved  to  be  unfounded.  It  is  now 
certain  that  there  is  no  such  great  body  dominating  the 
stellar  universe. 

387.  Maedler's  Hypothesis. —Another  less  improbable 
doctrine  is  that  there  is  a  general  revolution  of  the  mass 
of  stars  around  the  center  of  gravity  of  the  whole,  —  a 
revolution  nearly  in  the  plane  of  the  Milky  Way.     Some 
years  ago  Maedler,  in  his  speculations,  concluded  (though 
without  sufficient  reason)  that  this  center  of  gravity  of  the 
stellar  system  was  not  far  from  Alcyone,  the  brightest  of 
the  Pleiades,  and,  therefore,  that  this  star  was  in  a  sense 
the  "  central  sun  "  ;  and  the  idea  is  frequently  met  with 
in  popular  writings.     It  has  no  satisfactory  basis,  how- 
ever, nor  is  there  yet  proof  of  any  such  general  revolu- 
tion,  though  some  recent  investigations  rather  tend  to 
make  it  probable. 

388.  On  the  whole,  the  most  reasonable  view  seems  to 
be  that  the  stars  are  moving  much  as  bees  do  in  a  swarm, 
each   mainly  under  the  control  of  the  attraction  of  its 
nearest   neighbors,    though   influenced   more   or   less,    of 


348  LESSONS  IN  ASTRONOMY 

course,  by  that  of  the  general  mass.  From  a  study  of 
both  proper  and  radial  motions  it  has  been  found  that 
there  are  apparently  two  such  swarms  mixed  together  in 
what  we  call  our  universe.  The  stars  in  each  swarm  are 
flying  about  in  all  directions,  but  all  share  in  the  motion 
common  to  the  swarm.  The  two  swarms  are  moving  in 
nearly  opposite  directions. 

Probably  the  paths  of  the  stars  are  not  "  orbits  " ;  i.e., 
they  are  not  paths  which  return  into  themselves.  The 
forces  which  at  any  moment  act  upon  a  given  star  are 
so  nearly  balanced  that  its  motion  must  be  sensibly  in  a 
straight  line  for  thousands  of  years  at  a  time. 

COSMOGONY 

389.  One  of  the  most  interesting  topics  of  speculation 
relates  to  the  process  by  which  the  present  state  of  things 
has  come  about.  In  a  forest,  to  use  an  old  comparison  of 
Herschel's,  we  see  around  us  trees  in  all  stages  of  their 
life-history,  from  the  sprouting  seedlings  to  the  prostrate 
and  decaying  trunks  of  the  dead.  Is  the  analogy  appli- 
cable to  the  heavens,  and  can  we  hope  by  a  study  of  the 
present  condition  and  behavior  of  the  bodies  around  us  to 
come  to  an  understanding  of  their  past  history  and  prob- 
able future  ?  Possibly  to  some  extent.  But  human  life  is 
so  short  that  the  processes  of  change  are  hardly  perceptible, 
and  our  telescopes  and  spectroscopes  reveal  but  little  of 
the  "true  inwardness"  of  things,  so  that  speculation  is 
continually  baffled  and  its  results  can  seldom  be  accepted 
as  secure.  Still,  some  general  conclusions  seem  to  have 
been  reached  which  are  likely  to  be  true;  but  the  pupil 


GENESIS  OF  THE  PLANETARY  SYSTEM         349 

is  warned  that  they  are  not  to  be  regarded  as  established  in 
any  such  sense  as  the  law  of  gravitation  and  the  theory 
of  planetary  motion. 

In  a  general  way  we  may  say  that  the  gathering  of 
clouds  of  rarefied  matter  or  meteoritic  swarms  into  more 
compact  masses  under  the  force  of  gravitation,  the  produc- 
tion of  heat  by  this  shrinkage,  the  effect  of  this  heat  upon 
the  mass  itself  and  upon  neighboring  bodies, — these  prin- 
ciples cover  nearly  all  the  explanations  that  can  thus  far 
be  given  for  the  present  condition  of  the  heavenly  bodies. 

390.  Genesis  of  the  Planetary  System.  —  Our  planetary 
system  is  clearly  no  accidental  aggregation  of  bodies. 
Masses  of  matter  coming  haphazard  to  the  sun  would 
move  (as  comets  actually  do  move)  in  orbits  which,  though 
necessarily  conic  sections,  would  have  every  degree  of 
inclination  and  eccentricity.  In  the  planetary  system 
this  is  not  so.  Numerous  relations  exist  for  which  gravi- 
tation does  not  at  all  account,  and  for  which  the  mind 
demands  an  explanation. 

We  note  the  following  as  the  principal: 

1.  The  orbits  of  the  planets  are  all  nearly  circular  (i.e.,  never  very 
eccentric,  asteroids  excepted). 

2.  They  are  all  nearly  in  one  plane  (excepting  those  of  some 
of  the  asteroids). 

3.  The   revolution    of    all,    without    exception,    is    in    the   same 
direction. 

4.  There  is  a  curious  and  regular  progression  of  distances  (expressed 
by  Bode's  law,  which,  however,  breaks  down  with  Neptune). 

As  regards  the  planets  themselves : 

5.  The  plane  of  every  planet's  rotation  nearly  coincides  with  that 
of  its  orbit  (probably  excepting  Uranus). 


350  LESSONS  IN  ASTRONOMY 

6.  The  direction  of  rotation  is  the  same  as  that  of  the  orbital 
revolution  (excepting  probably  Uranus  and  Neptune). 

7.  The  plane  of  orbital  revolution  of  the  planet's  satellites  coin- 
cides nearly  with  that  of  the  planet's  rotation,  wherever  this  has 
been  ascertained. 

8.  The  direction  of  the  satellites'  revolution  also  usually  coincides 
with  that  of  the  planet's  rotation. 

9.  The  largest  planets  rotate  most  swiftly. 

391.  Now  this  arrangement  is  certainly  an  admirable  one 
for  a  planetary  system,  and  therefore  some  have  argued  that 
the  Deity  constructed  the  system  in  that  way,  perfect  from 
the  first.  But  to  one  who  considers  the  way  in  which 
other  perfect  works  usually  attain  their  perfection  —  their 
processes  of  growth  and  development  —  this  explanation 
seems  improbable.  It  appears  far  more  likely  that  the 
planetary  system  was  formed  by  growth  than  that  it  was 
built  outright. 

The  theory  which  in  its  main  features  is  now  generally 
accepted,  as  supplying  an  intelligible  explanation  of  the 
facts,  is  that  known  as  the  "nebular  hypothesis."  In  a 
more  or  less  crude  and  unscientific  form  it  was  first  sug- 
gested by  Swedenborg  and  Kant,  and  afterwards,  about 
the  beginning  of  the  present  century,  was  worked  out  in 
mechanical  detail  by  Laplace. 

It  was  formulated  before  the  discovery  of  the  great 
principles  of  the  "  conservation  of  energy,"  and  the  equiva- 
lence of  heat  to  other  forms  of  energy,  so  that  in  some 
respects  it  is  defective  and  doubtless  wrong.  The  main 
idea,  however,  that  our  system  was  once  an  incoherent 
mass  and  has  come  to  its  present  state  by  physical  pro- 
cesses, is  almost  certainly  correct,  and  forms  the  foundation 
of  all  current  speculation  upon  the  subject. 


THE  NEBULAR  HYPOTHESIS  351 

392.  Laplace's  Nebular  Hypothesis.  — He  maintained  or 
rather  suggested: 

(a)  That  at  some  time  in  the  past l  the  matter  which  is 
now  gathered  into  the  sun  and  planets  was  in  the  form  of 
a  "  nebula." 

(b)  This    nebula,    according   to   him,    was   a  cloud  of 
intensely  heated  gas  (questionable). 

(c)  Under  the  action  of  its  own  gravitation  the  nebula 
assumed  a  form  approximately  globular,  with  a  motion  of 
rotation,  the  whirling  motion  depending  upon  the  acci- 
dental differences  in  the  original  velocities  and  densities 
of  the  different  parts  of  the  nebula.     As  the  contraction 
proceeded  the  swiftness  of  the  rotation  would  necessarily 
increase  for  mechanical  reasons. 

(d)  In  consequence  of  its  whirling  motion  the  globe 
would   necessarily   become    flattened   at    the    poles   and 
ultimately,   as  the   contraction  went  on,  the  centrifugal 
force  at  the  equator  would  there  become  equal  to  gravity 
and  rings  of  nebulous  matter  would  be  detached  from  the 
central  mass,  like  the  rings  of  Saturn.     In  fact,  Saturn's 
rings  suggested  this  feature  of  the  theory. 

(e)  The  ring  thus  formed  would  for  a  time  revolve 
as  a  whole,  but  would  ultimately  break,  and  the  material 
would  collect  into  a  globe  revolving  around  the  central  nebula 
as  a  planet. 

1  As  to  the  origin  of  the  nebula  itself  he  did  not  speculate.  There  was 
no  assumption  on  his  part,  as  is  often  supposed,  that  the  matter  was  first 
created  in  the  nebulous  condition.  He  assumed  only  that,  as  the  egg  may 
be  taken  as  the  starting-point  in  the  life-history  of  an  animal,  so  the 
nebula  is  to  be  regarded  as  the  starting-point  of  the  life-history  of  the 
planetary  system.  He  did  not  raise  the  question  whether  the  egg  is,  or 
is  not,  older  than  the  hen. 


352  LESSONS  IN  ASTRONOMY 

Laplace  supposed  that  the  ring  would  revolve  as  if  it 
were  solid,  the  particles  at  the  outer  edge  moving  more 
swiftly  than  those  at  the  inner  (questionable).  If  this 
were  always  so,  the  planet  formed  would  necessarily  rotate 
in  the  same  direction  in  which  the  ring  had  revolved. 

(/)  The  planet  thus  formed  would  throw  off  rings  of  its 
own  and  so  form  for  itself  a  system  of  satellites. 

393.  This  theory  obviously  explains  most  of  the  facts 
of  the  solar  system,  which  were  enumerated  in  the  preced- 
ing article,  though  some  of  the  exceptional  facts  (such  as 
the  short  periods  of  the  satellites  of  Mars  and  the  retro- 
grade motions  of  those  of  Uranus  and  Neptune)  cannot  be 
explained  by  it  alone  in  its  original  form.  But  even  these 
exceptions  do  not  contradict  it,  as  is  sometimes  supposed. 

As  to  the  modifications  required  by  the  theory,  while 
they  alter  the  mechanism  of  the  development  in  some 
respects,  they  do  not  touch  the  main  results.  It  is  rather 
more  likely,  for  instance,  that  the  original  nebula  was  a 
cloud  of  ice-cold  dust  than  incandescent  gas  and  "fire 
mist,"  to  use  a  favorite  expression;  and  it  is  likely,  as 
suggested  by  the  spiral  nebulae,  that  planets  and  satellites 
were  often  separated  from  the  mother  orb  otherwise  than 
in  the  form  of  rings. 

Nor  is  it  possible  that  a  thin  wide  ring  could  revolve  in 
the  same  way  as  a  solid  mass ;  the  particles  near  the  inner 
edge  must  make  their  revolution  in  periods  much  shorter 
than  those  upon  the  circumference,  or  the  ring  would  tear 
to  pieces.  But  this  very  fact  makes  it  possible  to  account 
for  the  peculiar  backward  motion  of  the  satellites  of 
Uranus  and  Neptune,  thus  removing  one  of  the  main 
objections  to  the  theory  in  its  original  form, 


THE  METEORITIC  HYPOTHESIS  353 

Many  things  also  make  it  questionable  whether  the 
outer  planets  are  so  much  older  than  the  inner  ones,  as 
Laplace's  theory  would  indicate.  It  is  not  impossible  that 
they  may  even  be  younger. 

Our  limits  do  not  permit  us  to  enter  into  a  discussion  of  Darwin's 
"  tidal  theory  "  of  satellite  formation,  which  may  be  regarded  as,  in 
a  sense,  supplementary  to  the  nebular  hypothesis ;  nor  can  we  more 
than  mention  Faye's  proposed  modification  of  it.  According  to  him, 
the  inner  planets  are  the  oldest. 

394.  Lockyer's  Meteoritic  Hypothesis.1 — Sir  Norman 
Lockyer  has  of  late  vigorously  revived  a  theory  which  had 
been  from  time  to  time  suggested  before,  viz.,  that  all  the 
heavenly  bodies  in  their  present  state  are  mere  clouds  of 
meteors,  or  have  been  formed  by  the  condensation  of  such 
clouds;  and  it  is  an  interesting  fact,  as  Professor  G.  H. 
Darwin  has  recently  shown,  that  a  large  swarm  of  meteors 
in  which  the  individuals  move  swiftly  in  all  directions 
would,  in  the  long  run  and  as  a  whole,  behave  almost 
exactly,  from  a  mechanical  point  of  view,  in  the  same  way 
as  one  of  Laplace's  hypothetical  gaseous  nebulae.2 

The  spectroscopic  observations  upon  which  Sir  Norman  rests  his 
attempted  demonstration  are  many  of  them  very  doubtful ;  but  that 
does  not  really  discredit  the  main  idea,  except  so  far  as  the  question 
of  the  origin  and  nature  of  the  light  of  the  heavenly  bodies  is 

1  For  planetesimal  hypothesis  see  note  on  page  358. 

2  This  is  not  very  strange,  after  all.     According  to  the  modern  "  kinetic 
theory  of  gases"    (Rolfe's   "Physics,"  page  157),   a  meteor  cloud  is 
mechanically  just  the  same  thing  as  a  mass  of  gas  magnified.     The 
kinetic  theory  asserts  that  gas  is  only  a  swarm  of  minute  molecules,  the 
peculiar  gaseous  properties  depending  upon  the  collisions  of  these  mole- 
cules with  each  other  and  with  the  walls  of  the  inclosing  vessel. 


354  LESSONS  IN  ASTRONOMY 

concerned.  He  makes  the  light  depend  upon  the  collisions  between 
the  meteors,  and  finds  in  the  spectra  of  the  heavenly  bodies  evidence 
of  the  presence  of  materials  with  which  we  are  familiar  in  the  mete- 
orites which  fall  upon  the  earth's  surface.  These  identifications  are 
in  many  cases  questionable,  —  in  some  certainly  incorrect,  —  and  it 
seems  much  more  likely  that  the  luminosity  depends  to  a  great  degree 
upon  other  than  mere  mechanical  actions,  —  electrical  and  chemical 
for  instance. 

395.  Stars,  Star-Clusters,  and  Nebulae.  —  It  is  obvious 
that  the  nebular  hypothesis  in  all  its  forms  applies  to  the 
explanation  of  the  relations  of  these  different  classes  of 
bodies  to  each  other.     In  fact,  Herschel,  appealing  only  to 
the  "law  of  continuity,"  had  concluded,  before  Laplace 
published  his  theory,  that  the  nebulae  develop  sometimes 
into  clusters,  sometimes  into  double  or  multiple  stars,  and 
sometimes  into  single  stars.     He  showed  the  existence  in 
the  sky  of  all  the  intermediate  forms  between  the  nebula 
and  the  finished  star.     For  a  time,  about  the  middle  of  the 
last  century,  while  it  was  generally  believed  that  all  the 
nebulae  were  only  star-clusters,  too  remote  to  be  resolved 
by  existing  telescopes,  his  views  fell  rather  into  abeyance ; 
but  they  regained  acceptance  in  their  essential  features 
when  the  spectroscope  demonstrated  the  substantial  differ- 
ence between  gaseous  nebulae  and  the  star-clusters. 

396,  Conclusions  from  the  Theory  of  Heat.  —  Kant  and 
Laplace,  as  Newcomb  says,  seem  to   have  reached  their 
results  by  reasoning  forwards.     Modern  science  comes  to 
very  similar  conclusions  by  working  backwards  from  the 
present  state  of  things. 

Many  circumstances  go  to  show  that  the  earth  was  once 
much  hotter  than  it  now  is.  As  we  penetrate  below  the 
surface,  the  temperature  rises  nearly  a  degree  (Fahrenheit) 


CONCLUSIONS  FROM  THE  THEORY  OF  HEAT     355 

for  every  sixty  feet,  indicating  a  white  heat  at  the  depth 
of  a  few  miles  ;  the  earth  at  present,  as  Lord  Kelvin  says, 
"  is  in  the  condition  of  a  stone  that  has  been  in  the  fire  and 
has  cooled  at  the  surface." 

The  moon  bears  apparently  on  its  surface  the  marks  of 
the  most  intense  igneous  action,  but  seems  now  to  be 
entirely  chilled. 

The  planets,  so  far  as  we  can  make  out  with  the  tele- 
scope, exhibit  nothing  at  variance  with  the  view  that 
they  were  once  intensely  heated,  while  many  things  go 
to  establish  it.  Jupiter  and  Saturn,  Uranus  and  Neptune, 
do  not  seem  yet  to  have  cooled  off  to  anything  like  the 
earth's  condition. 

As  to  the  sun,  we  have  in  it  a  body  continuously  pour- 
ing forth  an  absolutely  inconceivable  quantity  of  heat  with- 
out any  visible  source  of  supply.  As  has  been  explained 
already  (Sec.  192),  the  only  rational  explanation  of  the 
facts  thus  far  presented  is  that  which  makes  it  a  huge, 
cloud-mantled  ball  of  elastic  substance  slowly  shrinking 
under  its  own  central  gravity,  and  thus  generating  heat.1 
A  shrinkage  of  about  two  hundred  feet  a  year  in  the 
sun's  diameter  will  account  for  the  whole  annual  output 
of  radiant  heat  and  light. 

397.  Age  of  the  System.  —  Looking  backward,  then,  and 
trying  to  imagine  the  course  of  time  and  of  events  reversed, 
We  see  the  sun  growing  larger  and  larger,  until  at  last  it 
has  expanded  to  a  huge  globe  that  fills  the  largest  orbit  of 

1  So  far  we  have  no  decisive  evidence  whether  the  sun  has  passed  its 
maximum  of  temperature  or  not.  Lockyer  thinks  its  spectrum  (resem- 
bling as  it  does  that  of  Capella  and  the  stars  of  the  second  class)  proves 
that  it  is  now  on  the  downward  grade  and  growing  cooler ;  but  others  do 
not  consider  the  evidence  conclusive. 


356  LESSONS  IN  ASTRONOMY 

our  system.  How  long  ago  this  may  have  been  we  can- 
not state  with  certainty.  If  we  could  assume  that  the 
amount  of  heat  yearly  radiated  by  the  solar  surface  had 
remained  constantly  the  same  through  all  those  ages,  and, 
moreover,  that  all  the  radiated  heat  came  solely  from  the 
slow  contraction  of  the  sun's  mass,  apart  from  any  con- 
siderable original  capital  in  the  form  of  a  high  initial 
temperature,  and  without  any  reenforcement  of  energy 
from  outside  sources,  —  if  we  could  assume  these  prem- 
ises, it  is  easy  to  show  that  the  sun's  past  history  must 
cover  about  15,000000  or  20,000000  years.  But  such 
assumptions  are  at  least  doubtful ;  and  if  we  discard 
them,  all  that  can  be  said  is  that  the  sun's  age  must  be 
greater,  and  probably  many  times  greater,  than  the  limit 
we  have  named. 

398.  Future  Duration  of  the  System. — Looking  forward, 
on  the  other  hand,  from  the  present  towards  the  future,  it 
is  easy  to  conclude  with  certainty  that  if  the  sun  con- 
tinues its  present  rate  of  radiation  and  contraction,  and 
if  contraction  is  its  only  source  of  heat,  it  must  within 
5,000000  or  10,000000  years  become  so  dense  that  its 
constitution  will  be  radically  changed.  Its  temperature 
will  fall,  and  its  function  as  a  sun  will  end.  Life  on  the 
earth,  as  we  know  life,  will  be  no  longer  possible  when  the 
sun  has  become  a  dark,  rigid,  frozen  globe.  At  least  this 
is  the  inevitable  consequence  of  what  now  seems  to  be  the 
true  account  of  the  sun's  condition  and  activity  if  nothing 
interferes  with  its  steady  and  inexorable  course. 

But  there  may  be  interference:  catastrophes  and  par- 
oxysms, sudden  changes  and  reversals  of  the  regular  course 
of  events  at  critical  moments,  collisions  and  explosions, 


THE   SYSTEM  NOT  ETERNAL  357 

are  certainly  possible  and  actually  occur,  as  the  phenom- 
ena of  the  solar  surface  and  temporary  stars  abundantly 
make  evident. 

399,  The  System  not  Eternal.  —  One  conclusion  seems 
to  be  clear :  that  the  present  system  of  stars  and  worlds  is 
not  an  eternal  one.  We  have  before  us  everywhere  evi- 
dence of  continuous,  irreversible  progress  from  a  definite 
beginning  towards  a  definite  end.  Scattered  particles  and 
masses  are  gathering  together  and  condensing,  so  that  the 
great  grow  continually  larger  by  capturing  and  absorbing 
the  smaller.  At  the  same  time  the  hot  bodies  are  losing 
their  heat  and  distributing  it  to  the  colder  ones,  so  that 
there  is  an  unremitting  tendency  towards  a  uniform,  and 
therefore  useless,  temperature  throughout  our  whole  uni- 
verse ;  for  heat  is  available  as  energy  (i.e.,  it  can  do  work) 
only  when  it  can  pass  from  a  warmer  body  to  a  colder 
one.  The  continual  warming  up  of  cooler  bodies  at  the 
expense  of  hotter  ones  always  means  a  loss,  therefore, 
not  of  energy,  for  that  is  indestructible,  but  of  available 
energy.  To  use  the  ordinary  technical  term,  energy  is 
continually  dissipated  by  the  processes  which  constitute 
and  maintain  life  on  the  universe.  This  dissipation  of 
energy  can  have  but  one  ultimate  result,  that  of  absolute 
stagnation  when  the  temperature  has  become  everywhere 
the  same. 

If  we  carry  our  imagination  backwards,  we  reach  "a 
beginning  of  things,"  which  has  no  intelligible  antecedent; 
if  forwards,  we  come  to  an  end  of  things  in  dead  stagnation. 
That  in  some  way  this  end  of  things  will  result  in  a  "  new 
heavens  and  a  new  earth"  is,  of  course,  probable,  but 
science  as  yet  can  present  no  explanation  of  the  method. 


358  LESSONS  IN  ASTRONOMY 

NOTE  TO  ARTICLE  394 

The  Planetesimal Hypothesis. — A  new  form  of  the  meteoric  theory, 
known  as  the  "  planetesimal  hypothesis,"  has  been  recently  proposed 
and  developed  in  this  country  by  Chamberlin  and  Moulton,  who 
consider  that  they  have  demonstrated  the  falsity  of  Laplace's  "  ring 
theory." 

They  assume  as  the  origin  of  the  solar  system,  instead  of  the  gas- 
eous globe  of  Laplace,  a  spiral  nebula  (like  that  shown  by  the  figure 
on  page  340)  composed  of  gas,  carrying  mingled  with  it  multitudes 
of  little  solid  masses  (planetesimals)  moving  around  the  center, 
generally  in  the  same  direction,  but  in  orbits  that  vary  in  inclina- 
tion, eccentricity,  and  period,  and  are  subject  to  continual  perturba- 
tion. There  results  a  very  slow  accretion  of  the  planetesimals  into 
planets,  with  very  little  development  of  heat,  since  the  relative 
velocities  of  the  colliding  bodies  are  very  small. 

A  great  advantage  of  this  theory  is  that  it  allows  time  enough  to 
satisfy  the  most  exorbitant  demands  of  geology  and  biology,  besides 
evading  nearly  all,  if  not  all,  of  the  difficulties  that  embarrass  the 
original  nebular  hypothesis. 


APPENDIX 


ASTRONOMICAL  INSTRUMENTS 

The  Celestial  Globe  —  The  Telescope  :  Simple,  Achromatic,  and  Reflecting 
—  The  Equatorial  —  The  Filar  Micrometer  —  The  Transit-Instrument  — 
The  Clock  and  Chronograph  —  The  Meridian  Circle  — The  Sextant 

400.  The  Celestial  Globe.  —  The  celestial  globe  is  a  ball, 
usually  of  papier-mache,  upon  which  are  drawn  the  circles  of 
the  celestial  sphere  and  a  map  of  the  stars.  It  is  ordinarily 
mounted  in  a  framework  which  represents  the  horizon  and 
the  meridian  in  the  manner  shown  in  Fig.  98. 

The  "  horizon,"  HH'  in  the  figure,  is  usually  a  wooden  ring 
three  or  four  inches  wide  and  perhaps  three-quarters  of  an 
inch  thick,  directly  supported  by  the  pedestal.  It  carries 
upon  its  upper  surface  at  the  inner  edge  a  circle  marked  with 
degrees  for  measuring  the  azimuth  of  any  heavenly  body, 
and  outside  this  the  so-called  zodiacal  circles,  which  give 
the  sun's  longitude  and  the  equation  of  time  for  every  day 
of  the  year. 

The  meridian  ring,  MM',  is  a  circular  ring  of  metal  which 
carries  the  bearings  upon  which  the  globe  revolves.  Things 
are  so  arranged,  or  o.ught  to  be,  that  the  mathematical  axis 
of  the  globe  is  exactly  in  the  same  plane  as  the  graduated  face 
of  the  ring,  which  is  divided  into  degrees.  The  meridian  ring 
is  held  underneath  the  globe  by  a  support,  with  a  clamp  which 
enables  us  to  fix  it  securely  in  any  desired  position. 

The  surface  of  the  globe  is  marked  first  with  the  celestial 
equator,  next  with  the  ecliptic  crossing  the  equator  at  an 

359 


360 


APPENDIX 


angle  of  23|°  at  X  (as  the  figure  is  drawn,  not  the  vernal),  and 
each  of  these  circles  is  divided  into  degrees.  The  equinoctial 
and  solstitial  colures  X  and  PE  are  also  always  represented, 
E  being  the  pole  of  the  ecliptic.  As  to  the  other  circles, 
usage  differs.  The  ordinary  way  at  present  is  to  mark  the 
globe  with  twenty-four  hour-circles  15°  apart  (the  colures, 
Sec.  117,  being  four  of  them),  and  with  parallels  of  declina- 
tion 10°  apart.  On  the  surface  of  the  globe  are  plotted  the 

positions  of  the  stars 
and  the  outlines  of 
the  constellations. 

It  is  perhaps  worth 
noting  that  many  of  the 
spirited  figures  of  the 
constellations  upon  our 
present  globes  are  copied 
from  designs  drawn  by 
Albert  Dtirer  for  a  star- 
map  published  in  his 
time. 

The  Hour-Index  is 
usually  a  small  circle 
of  thin  metal,  about 
four  inches  in  diam- 
eter, which  is  fitted 
to  the  northern 
pole  of  the  globe 

with  a  stiffish  friction,  so  that  it  can  be  set  like  the  hands 
of  a  clock,  and  when  once  set  will  turn  with  the  globe 
without  shifting. 

On  some  globes  a  hand  like  a  clock-hand  is  used,  showing  the  hour 
on  a  circle  engraved  on  the  surface  of  the  globe  itself.  This  is  the 
case  with  the  globe  shown  in  the  figure. 


FIG.  98.  — The  Celestial  Globe 


THE  CELESTIAL  GLOBE  361 

401,  To  "  rectify  "  a  Globe,  —  i.e.,  to  set  it  so  as  to  show 
the  aspect  of  the  heavens  at  any  time : 

1.  Elevate  the  north  pole  P  of  the  globe  to  an  angle  equal 
to  the  observer's  north  latitude  by  means  of  the  graduation  on 
the  meridian  ring,  and  clamp  the  ring  securely. 

If  the  observer  is  south  of  the  equator,  the  south  pole,  of  course, 
must  be  elevated  instead  of  the  north. 

2.  Look  up  the  day  of  the  month  on  the  horizon  of  the 
globe,  and  opposite  to  the  day  find  on  the  zodiacal  circle  the 
sun's  longitude  for  that  day. 

3.  On  the   ecliptic   (upon  the  surface  of   the    globe)  find 
the  degree  of  longitude  thus  indicated,  and  bring  it  to  the 
graduated  face  of  the  meridian  ring.     The  globe  is  thus  set 
to  correspond  to  apparent  noon  of  the  day  in  question. 

It  may  be  well  to  mark  the  place  of  the  sun  temporarily  with  a  bit 
of  paper  gummed  on  at  the  proper  place  in  the  ecliptic.  It  can  easily 
be  wiped  off  after  using. 

4.  Hold  the  globe  fast  so  as  to  keep  the  place  of  the  sun 
exactly  on  the  meridian,  and  turn  the  hour-index  until  it  shows 
the  mean  time  of  apparent  noon  (i.e.,  12h  ±  the  equation  of 
time  given  on  the  wooden  horizon  for  the  day  in  question). 

If  standard  time  is  used,  the  hour-index  must  be  set  to  the  standard 
time  for  apparent  noon  instead  of  the  local  mean  time. 

5.  Finally,  turn  the  globe  upon  its  axis  until  the  hour- 
index  shows  the  hour  for  which  it  is  to  be  set.     The  globe 
will  then  represent  the  true  aspect  of  the  heavens  at  that  time. 

The  hour-index  ought  to  keep  its  position  unchanged  while  the 
globe  is  revolved,  but  the  observer  must  watch  to  see  that  it  does 
not  shift ;  many  globes  are  faulty  in  this  respect. 

The  positions  of  the  moon  and  planets  are  not  given  by  this  opera- 
tion, since  they  have  no  fixed  places  in  the  sky  and  therefore  cannot 


362  APPENDIX 

be  put  in  by  the  globe  maker.  If  one  wants  them  represented,  he 
must  look  up  their  right  ascensions  and  declinations  in  some  almanac 
and  mark  the  proper  places  on  the  globe  with  bits  of  wax  or  paper. 

TELESCOPES 

402.  Telescopes  are  of  two  kinds,  • —  refracting  and  reflecting. 
The  refractor  was  first  invented  early  in  the  seventeenth 

century  and  is  much  more  used,  but  the  largest  instruments 
ever  made  are  reflectors.  In  both,  the  fundamental  principle 
is  the  same.  The  large  lens  of  the  instrument  (or  else  its 
concave  mirror)  forms  a  real  image  of  the  object  looked  at, 
and  this  image  is  then  examined  and  magnified  by  the  eye- 
piece, which  in  principle  is  only  a  magnifying-glass. 

In  the  form  of  instrument,  however,  which  was  originally  devised 
by  Galileo  and  is  still  used  as  the  "  opera-glass,"  the  rays  from  the 
object-glass  are  intercepted  and  brought  to  parallelism  by  a  concave 
lens  which  serves  as  an  eye-glass,  before  they  form  the  image.  Tele- 
scopes of  this  construction  are  never  made  of  much  power,  being 
inconvenient  on  account  of  the  smallness  of  the  field  of  view. 

403.  The  Simple  Refracting    Telescope.  —  This  consists 
essentially,  as  shown  in  Fig.  99,  of  two  convex  lenses :  one, 
the  object-glass  A,  of  large  size  and  long  focus ;  the  other,  the 
eye-glass  B,  of  short  focus,  —  the  two  being  set  at  a  distance 
nearly  equal  to  the  sum  of  their  focal  lengths.     Kecalling  the 
optical  principles  relating  to  the  formation  of  images  by  lenses, 
we  see  that  if  the  instrument  is  pointed  towards  the  moon,  for 
instance,  all  the  rays  that  strike  the  object-glass  from  the  top 
of  the  crescent  will  be  collected  to  a  focus  at  a,  while  those 
from  the  bottom  will  come  to  a  focus  at  b ;  and  correspondingly 
with  rays  from  the  other  points  on  the  surface  of  the  moon. 
We  shall,  therefore,  get  in  the  "  focal  plane  "  of  the  object- 
glass  a  small  inverted  "  image  "  of  the  moon.     The  image  is 
a  real  one,  i.e.,  the  rays  really  meet  at  the  focal  points,  so  that 


TELESCOPES  363 

if  we  insert  a  photographic  plate  in  the  focal  plane  at  ab  and 
properly  expose  it,  we  shall  get  a  picture  of  the  object.  The 
size  of  the  picture  will  depend  upon  the  apparent  angular 
diameter  of  the  object  and  the  distance  from  the  object-glass 
to  the  image  ab. 

If  the  focal  length  of  the  lens  A  is  ten  feet,  then  the  image  of 
the  moon  (31'  in  apparent  diameter)  will  be  a  little  more  than  one 
inch  in  linear  diameter. 

404,  Magnifying  Power.  —  If  we  use  the  naked  eye  we 
cannot  see  the  image  distinctly  from  a  distance  much  less 
than  a  foot,  but  if  we  use  a  magnifying-lens  of,  say,  one  inch 
focus,  we  can  view  it  from  a  distance  of  only  an  inch  and 
it  will  look  correspondingly  larger.  Without  stopping  to 


FIG.  99.  —  The  Simple  Refracting  Telescope 

prove  the  principle,  we  may  say  that  the  magnifying  power 
is  simply  equal  to  the  quotient  obtained  by  dividing  the  focal 
length  of  the  object-glass  by  that  of  the  eye-lens. 

It  is  to  be  noted,  however,  that  a  magnifying  power  of  unity  is 
sometimes  spoken  of  as  "no  magnifying  power  at  all,"  since  the 
image  appears  of  the  same  size  as  the  object. 

The  magnifying  power  of  a  telescope  is  changed  at  pleasure  by 
simply  interchanging  the  eyepieces,  of  which  every  telescope  of  any 
pretensions  always  has  a  considerable  stock  giving  various  powers. 
These  usually  contain  two  or  more  lenses  in  order  to  give  good 
definition  over  a  larger  field  than  can  be  obtained  with  a  single-lens 
eyepiece.  (See  Sec.  409.) 

405.  Brightness  of  the  Image.  —  This  depends  not  upon 
the  focal  length  of  the  object-glass,  but  upon  its  diameter,  or, 


364  APPENDIX 

more  strictly,  its  area.  If  we  estimate  the  diameter  of  the 
pupil  of  the  eye  at  one-fifth  of  an  inch,  as  it  is  usually  reck- 
oned, then  (neglecting  the  loss  from  want  of  perfect  transpar- 
ency in  the  lenses)  a  telescope  one  inch  in  diameter  collects 
into  the  image  of  a  star  25  times  as  much  light  as  the  naked 
eye  receives ;  and  the  great  Yerkes  telescope  of  40  inches  in 
diameter,  40,000  times  as  much,  or  about  35,000  after  allow- 
ing for  the  losses.  The  amount  of  light  is  proportional  to 
the  square  of  the  diameter  of  the  object-glass. 

The  apparent  brightness  of  an  object  which,  like  the  moon 
or  a  planet,  shows  a  disk,  is  not,  however,  increased  in  any 
such  ratio,  because  the  light  gathered  by  the  object-glass  is 
spread  out  by  the  magnifying  power  of  the  eyepiece.  But 
the  total  quantity  of  light  in  the  image  of  the  object  greatly 
exceeds  that  which  is  available  for  vision  with  the  naked 
eye,  and  objects  which,  like  the  stars,  are  mere  luminous 
points  have  their  brightness  immensely  increased,  so  that 
with  the  telescope  millions  otherwise  invisible  are  brought 
to  light.  With  the  telescope,  also,  the  brighter  stars  are  easily 
seen  in  the  daytime. 

406.  The  Achromatic  Telescope.  —  A  single  lens  cannot 
bring  the  rays  which  emanate  from  a  single  point  in  the  object 
to  any  exact  focus,  since  the  rays  of  each  different  color  are 
differently  refracted,  —  the  blue  more  than  the  green,  and  this 
more  than  the  red.  In  consequence  of  this  so-called  "chro- 
matic aberration"  the  simple  refracting  telescope  is  a  very 
poor 1  instrument. 

About  1760  it  was  discovered,  in  England,  that  by  making 
the  object-glass  of  two  or  more  lenses  of  different  kinds  of 

1  By  making  it  extremely  long  in  proportion  to  its  diameter,  the  indis- 
tinctness of  the  image  is  considerably  diminished ;  and  in  the  middle  of  the 
seventeenth  century  instruments  more  than  100  feet  in  length  were  used 
by  Huyghens  and  others.  Saturn's  rings  and  several  of  his  satellites  were 
discovered  with  instruments  of  this  kind. 


TELESCOPES  365 

glass,  the  chromatic  aberration  can  be  nearly  corrected. 
Object-glasses  so  made  —  none  others  are  now  in  common 
use  —  are  called  achromatic.  In  practice,  only  two  lenses  are 
ordinarily  used  in  the  construction  of  an  astronomical  glass, 
—  a  convex  of  crown-glass  and  a  concave  of  ^m^-glass,  the 
curves  of  the  two  lenses  and  the  distances  between  them  being 
so  chosen  as  to  give  the  best  attainable  correction  of  the 
"  spherical "  aberration  (see  any  Physics  textbook),  as  well 
as  of  the  chromatic. 

407.  Achromatism  not  Perfect.  —  It  is  not  possible  with 
the  kinds  of  glass  ordinarily  obtainable  to  get  a  perfect  cor- 
rection of  color      Even  the  best  achromatic  telescopes  show  a 
purple  halo  around  the  image  of  a  bright  star,  which,  though 
usually   regarded    as    "very   beautiful7'    by   tyros,    seriously 
injures  the  definition  and   is  especially  obnoxious   in  large 
instruments. 

This  imperfection  of  achromatism  makes  it  impossible  to  get 
satisfactory  photographs  with  an  ordinary  visual  telescope. 

The  rays  of  light  most  efficient  in  impressing  the  image  upon  the 
photographic  plate  are  the  blue  and  violet,  which  in  the  visual 
object-glass  are  left  to  wander  wildly,  their  effect  upon  the  eye  being 
slight  as  compared  with  that  of  the  yellow  rays. 

For  photographic  purposes  we  may  use  an  object-glass  specially 
figured  for  the  photographic  rays  (but  then  the  telescope  is  useless 
for  visual  work) ;  or  we  may  combine  with  the  visual  object-glass  a 
third  lens,  known  as  a  "photographic  corrector,"  to  be  used  only 
with  the  camera;  or  we  may  use  with  the  visual  object-glass  a 
colored  screen  to  cut  out  the  violet  rays,  and  photographic  plates 
which  have  been  specially  sensitized  for  the  remaining  light.  The 
last  of  these  methods,  while  very  convenient  and  inexpensive, 
involves  a  great  loss  of  light  and  cannot  be  used  advantageously  for 
very  faint  objects. 

408.  Diffraction  and  Spurious  Disks. — Even  if  a  lens  were 
absolutely  perfect  as  regards  the  correction  of  aberrations, 


366  APPENDIX 

both  spherical  and  chromatic,  it  would  still  be  unable  to  give 
vision  absolutely  distinct.  Since  light  consists  of  waves  of 
finite  length,  the  image  of  a  luminous  point  can  never  be  also 
SL  point)  but  must  of  mathematical  necessity  be  a  hazy-edged 
disk  of  finite  diameter  surrounded  by  a  series  of  "  diffraction  " 
rings.  The  diameter  of  the  "  spurious  disk  "  of  a  star,  as  it  is 
called,  varies  inversely  with  the  diameter  of  the  object-glass  : 
the  larger  the  telescope,  the  smaller  the  image  of  a  star  with 
a  given  magnifying  power. 

With  a  good  telescope  and  a  power  of  about  30  to  thfc  inch  of 
aperture  (120  for  a  4-inch  telescope)  the  image  of  a  star,  when  the 
air  is  steady  (a  condition  unfortunately  seldom  fulfilled),  should  be 

a  clean,  round  disk  with  a  bright 
ring  around  it,  separated  from  the 
disk  by  a  clear  black  space. 
According  to  Dawes,  the  disk  of 
a  star  with  a  4|-inch  telescope 
should  be  about  1"  in  diameter; 


E  Z2Z 
^z^^^^lj 


FIG.  100.  -Telescope  Eyepieces        ^    a    9-inch   instrument   0".5, 

and  \"  for   a  36-inch  glass.     In  a 

4f-inch  telescope,  therefore,  the  two  disks  of  a  double  star  with 
a  distance  of  V  between  centers  would  be  just  in  contact  ;  with  the 
Yerkes  telescope  this  would  be  the  case  if  the  distance  were  0".l  ; 
and  in  this  fact  lies  much  of  the  superiority  of  great  telescopes. 

409,  Eyepieces.  —  For  some  purposes  the  simple  convex 
lens  is  the  best  "  eyepiece  "  possible  ;  but  it  performs  well 
only  for  a  small  object,  like  a  close  double  star,  placed  exactly 
in  the  center  of  the  field  of  view.  Generally,  therefore,  we 
employ  "  eyepieces  "  composed  of  two  or  more  lenses,  which 
give  a  larger  field  of  view  than  a  single  lens,  and  define  satis- 
factorily over  the  whole  extent  of  the  field.  They  fall  into 
two  general  classes,  the  positive  and  the  negative. 

The  positive  eyepieces  are  much  more  generally  useful.  They  act 
as  simple  magnifying-glasses,  and  can  be  taken  out  of  the  telescope 


TELESCOPES  367 

and  used  as  hand  magnifiers  if  desired.  The  image  of  the  object 
formed  by  the  object-glass  lies  outside  o/this  kind  of  eyepiece,  between 
it  and  the  object-glass. 

In  the  negative  eyepiece,  on  the  other  hand,  the  rays  from  the 
object-glass  are  intercepted  by  the  so-called  «  field-lens  "  before  reach- 
ing the  focus,  and  the  image  is  formed  between  the  two  lenses  of  the 
eyepiece.  It  cannot,  therefore,  be  used  as  a  hand  magnifier. 

Fig.  100  shows  the  two  most  usual  forms  of  eyepiece,  but  there 
are  many  others. 

These  eyepieces  show  the  object  in  an  inverted  position ;  but 
this  is  of  no  importance  as  regards  astronomical  observations. 

410.  Reticle.  —  When  the  telescope  is  used  for  pointing 
upon  an  object,  as  it  is  in  most  astronomical  instruments,  it 
must  be  provided  with  a  "  reticle  "  of  some  sort.     The  simplest 
form  is  a  metallic  frame  with  spider  lines  stretched  across  it, 
the  intersection  of  the  spider  lines  being  the  point  of  reference. 
This  reticle  is  placed  not  at  or  near  the  object-glass,  as  is 
often  supposed,  but  in  its  focal  plane,  as  ab  in  Fig.  99.    Some- 
times a  glass  plate  with  fine  lines  ruled  upon  it  is  used 
instead  of  spider  lines.     Some  provision  must  be  made  for 
illuminating  the  lines,  or  "  wires/7  as  they  are  usually  called, 
by  reflecting  into  the  instrument  a  faint  light  from  a  lamp 
suitably  placed. 

411.  The  Reflecting  Telescope.  — About  1670,  when  the  chro- 
matic aberration  of  refractors  first  came  to  be  understood  (in 
consequence  of  Newton's  discovery  of  the  "  decomposition  of 
light"),  the  reflecting  telescope  was  invented.     For  nearly 
150  years  it  held  its  place  as  the  chief  instrument  for  star- 
gazing, until  about  1820,  when  large  achromatics  began  to 
be  made.     There  are  several  varieties  of  reflecting  telescope, 
differing  in  the  way  in  which  the  image  formed  by  the  mirror 
is  brought  within  reach  of  the  magnifying  eyepiece. 

Until  about  1870  the  large  mirror  (technically  "  speculum  ") 
was  always  made  of  speculum  metal,  a  composition  of  copper 


368  APPENDIX 

and  tin.  It  is  now  usually  made  of  glass,  silvered  on  the 
front  by  a  chemical  process.  When  new,  these  silvered  films 
reflect  much  more  light  than  the  old  speculum  metal  :  they 
tarnish  rather  easily,  but  fortunately  can  be  easily  renewed. 

412.  Large  Telescopes.  —  The  largest  telescopes  ever  made  have 
been  reflectors.     At  the  head  stands  the  enormous  instrument  of 
the  Mt.  Wilson  Solar  Observatory,  100  inches  in  diameter,  mounted 
in  1917.     At  Victoria,  B.C.,  there  is  a  72-inch  mirror  which  was 
completed  in  1915,  equal  in  size,  but  superior  in  power,  to  Lord 
Rosse's  great  reflector,  made  in  1842,  for  many  years  the  largest. 
Keeler's  work  with  the  3-foot  Crossley  reflector  at  the  Lick  Observ- 
atory opened  a  new  era  in  the  photography  of  nebulae   and  star 
clusters,  and   the    still   more  wonderful   photographs   obtained   at 
Mt.  Wilson  with  Rltchey's  5-foot  mirror  show  the  great  possibilities 
of  the  reflector  in  this  line  of  work.     One  of  the  most  famous 
instruments  of  this  class  is  the  great  4-foot  reflector  at  Paris. 

Of  the  refractors,  the  largest  is  that  of  the  Yerkes  Observatory  at 
Williams  Bay,  Wisconsin,  with  an  object-glass  40  inches  in  diameter 
and  a  tube  nearly  70  feet  long.  The  next  in  size  is  the  telescope  of 
the  Lick  Observatory,  which  has  an  aperture  of  36  inches.  Next 
to  this  come  the  telescopes  at  Potsdam,  Pulkowa,  Meudon,  Nice, 
and  Allegheny,  with  apertures  of  about  30  inches;  the  Greenwich 
telescope,  28  inches;  the  Vienna  telescope,  27  inches;  the  two  tele- 
scopes at  Washington  and  the  University  of  Virginia,  26£  inches; 
and  four  or  five  others  with  apertures  of  from  26  to  23  inches, 
at  Cambridge  (England),  Greenwich,  Paris,  and  Princeton.  More 
than  half  of  these  large  object-glasses  were  made  by  the  Clarks  of 
Cambridge  (U.S.). 

413.  Relative  Advantages  of  Reflectors  and  Refractors.  —  There 
is  no  little  discussion  on  this  point,  each  form  of  instrument  having 
its  earnest  partisans. 

In  favor  of  the  reflector  we  have  first,  its  cheapness  and  compara- 
tive ease  of  construction,  since  there  is  but  one  surface  to  grind  and 
polish,  as  against  four  in  an  achromatic  object-glass ;  second,  the  fact 
that  reflectors  can  be  made  larger  than  refractors ;  third,  the  reflector 
is  absolutely  achromatic,  and  this  gives  it  an  immense  advantage  in 


THE  EQUATORIAL 


369 


certain  lines  of  astronomical  photography  (as,  for  instance,  in  that 
of  the  nebulae)  and  of  spectroscopy. 

On  the  other  hand,  a  refractor  gives  a  much  brighter  image  than 
a  reflector  of  the  same  size ;  it  also  generally  defines  much  better, 
because,  for  optical  reasons  into  which  we  cannot  enter  here,  any 
slight  distortion  or  malformation  of  the  speculum  of  a  reflector  dam- 
ages the  image  many  times  more  than  the  same  amount  of  distortion 
of  an  object-glass.  Then  a  lens  hardly  deteriorates  at  all  with  age, 
while  a  speculum  soon  tarnishes,  and  must  be  resilvered  or  repolished 
every  few  years.  The  lens  gives  also  a 
wider  field  of  good  definition. 

Finally,    as    a    rule,    refractors    are  T 

lighter  and  more  convenient  than  reflect- 
ors of  equal  power. 

414.  Mounting  of  a  Telescope, 
—  the  Equatorial.  —  A  telescope, 
however  excellent  optically,  is  not 
of  much  use  unless  firmly  and  con- 
veniently mounted.1 

At  present  some  form  of  equatorial 
mounting  is  practically  universal. 
Fig.  101  represents  schematically 
the  ordinary  arrangement  of  the 
instrument.  Its  essential  feature 
is  that  its  "  principal  axis  "  (i.e.,  the 
one  which  turns  in  fixed  bearings  attached  to  the  pier,  and  is 
called  the  polar  axis)  is  placed  parallel  to  the  earth's  axis, 
pointing  to  the  celestial  pole,  so  that  the  circle  H,  attached  to 
it,  is  parallel  to  the  celestial  equator.  This  circle  is  some- 
times called  the  hour-circle,  sometimes  the  right-ascension 

1  We  may  add  that  it  must,  of  course,  be  mounted  where  it  can  be 
pointed  directly  at  the  stars,  without  any  intervening  window-glass 
between  it  and  the  object.  We  have  known  purchasers  of  telescopes  to 
complain  bitterly  because  they  could  not  see  Saturn  well  through  a  closed 
window. 


FIG.  101.  —  The  Equatorial 


370 


APPENDIX 


FIG.  102.  —  Great  Double  Equatorial,  Visual  and  Photographic,  of  the 
Potsdam  Astrophysical  Observatory 

circle.  At  the  extremity  of  the  polar  axis  a  "sleeve"  is 
fastened,  which  carries  within  it  the  declination  axis  D,  and 
to  this  declination  axis  is  attached  the  telescope  tube  T,  and 
also  the  declination  circle  C. 


THE  MICROMETER  371 

The  advantages  of  this  mounting  are  very  great.  In  the 
first  place,  when  the  telescope  is  once  pointed  upon  an  object 
it  is  not  necessary  to  move  the  declination  axis  at  all  in  order 
to  keep  the  object  in  the  field,  but  only  to  turn  the  polar  axis 
with  a  perfectly  uniform  motion,  which  motion  can  be,  and 
usually  is,  given  by  clockwork  (not  shown  in  the  figure). 

In  the  next  place,  it  is  very  easy  to  find  an  object  even 
if  invisible  to  the  eye  (like  a  faint  comet,  or  a  star  in  the 


FIG.  103.  —  Filar-Position  Micrometer 
By  Warner  and  Swasey 

daytime)  provided  we  know  its  right  ascension  and  declination, 
and  have  the  sidereal  time,  —  a  sidereal  clock  or  chronometer 
being  an  indispensable  accessory  of  the  instrument. 

Fig.  81,  Sec.  337,  represents  another  form  of  equatorial  mounting, 
which  has  been  adopted  for  some  of  the  instruments  of  the  photo- 
graphic campaign. 

415.  The  Micrometer.  —  This  is  an  instrument  for  meas- 
uring small  angles,  usually  not  exceeding  15'  or  20'.  Various 


372 


APPENDIX 


kinds  are  employed,  all  of  them  small  pieces  of  apparatus, 
which,  when  used,  are  secured  to  the  eye  end  of  a  telescope. 
The  most  common  is  the  parallel-wire  micrometer,  which  is  a 

pair  of  parallel  spider  threads, 
one  or  both  of  which  can  be 
moved  with  a  fine  screw  with 
a  graduated  head,  so  that  the 
distance  between  the  two 
"wires"  can  be  varied  at 
pleasure  and  then  "read  off" 
by  looking  at  the  micrometer 
head.  Fig.  103  represents  such 
an  instrument  to  be  attached 
to  a  telescope ;  the  threads 
are  in  the  box  BB,  and  are 
viewed  through  the  eyepiece. 
FIG.  104. -The  Transit-Instrument  416«  The  Transit-Instru- 

ment  (Fig.  104).  —  This  con- 
sists of  a  telescope  carrying  at  the  eye  end  a  reticle,  and 
mounted  on  a  stiff  axis  with  pivots 
that  are  perfectly  equal  and  cylindri- 
cal. They  turn  in  Y's  which  are 
firmly  set  upon  some  sort  of  frame- 
work or  on  the  top  of  solid  piers,  and 
so  placed  that  the  axis  will  be  exactly 
east  and  west  and  precisely  level. 
When  the  telescope  is  turned  on  its 
axis,  the  middle  "  wire  "  of  the  reticle, 
if  everything  is  correctly  adjusted, 
will  follow  the  celestial  meridian, 
and  whenever  a  star  crosses  the  wire 
we  know  that  it  is  exactly  on  the  meridian.  Instead  of  a 
single  wire  the  reticle  generally  contains  a  number  of  wires 
equally  spaced,  as  shown  in  Fig.  105.  The  observer  notes 


FIG.  105.  —  Reticle  of  the 
Transit-Instrument 


TIMEPIECES  373 

by  his  timepiece  the  instant  at  which  the  object  crosses 
each  of  the  wires,  and  the  mean  of  the  observations  is  taken 
as  giving  the  moment  when  the  star  crossed  the  middle 
wire. 

A  delicate  spirit-level,  to  be  placed  on  the  pivots  and  test 
the  horizontality  of  the  axis,  is  an  indispensable  accessory. 

So  far  as  the  theory  of  the  instrument  is  concerned,  a  gradu* 
ated  circle  is  not  essential ;  but  practically  it  is  necessary  to 
have  one  attached  to  the  axis  in  order  to  enable  the  observer 
to  set  the  instrument  to  the  proper  altitude  in  preparing  for 
the  observation  of  a  star. 

417.  The  Astronomical  Clock,  Chronometer,  and  Chrono- 
graph. —  A  good  timepiece  is  an  essential  adjunct  of  the 
transit-instrument,  and  equally  so  of  most  other  astronom- 
ical instruments.  The  invention  of  the  pendulum  clock  by 
Huyghens  was  almost  as  important  an  event  in  the  history 
of  practical  astronomy  as  that  of  the  telescope  itself. 

The  astronomical  clock  differs  in  no  essential  respect  from 
any  other,  except  that  it  is  made  with  extreme  care  and  has  a 
"  compensated  "  pendulum  so  constructed  that  the  rate  of  the 
clock  will  not  be  affected  by  changes  of  temperature.  It  is 
almost  invariably  made  to  beat  seconds,  and  usually  has  its 
face  divided  into  twenty-four  hours  instead  of  twelve. 

Excellence  in  a  clock  consists  essentially  in  the  constancy 
of  its  "rate"  ;  i.e.,  it  should  gain  or  lose  precisely  the  same 
amount  each  day,  and  as  a  matter  of  convenience  the  daily 
rate  should  be  small,  not  to  exceed  a  second  or  two.  The 
rate  is  adjusted  by  slightly  raising  or  lowering  the  pendulum 
bob,  or  putting  little  weights  upon  a  small  shelf  attached  to 
the  rod;  the  "error,"  when  necessary,  is  corrected  by  simply 
setting  the  hands. 

The  error  of  a  timepiece  is  the  difference  between  the  time  shown 
by  the  clock-face  and  the  true  time  at  the  moment ;  the  rate  is  the 
amount  it  gains  or  loses  in  twenty-four  hours. 


874 


APPENDIX 


The  chronometer  is  simply  a  carefully  made  watch  and 
has  the  advantage  of  portability,  though  in  accuracy  it 
cannot  quite  compete  with  a  well  made  clock. 

Formerly  transit-instrument  observations  were  made  by 
simply  noting  with  eye  and  ear  the  time  indicated  by  the 

clock  at  the  moment  when 
the  star  observed  was 
crossing  the  wire  or  reti- 
cle. A  skillful  observer 
can  do  this  within  about 
a  tenth  of  a  second.  At 
present  the  observer  usu- 
ally presses  a  telegraph- 
key  at  the  moment  of  the 
transit  and  so  telegraphs 
the  instant  to  an  instru- 
ment called  a  chronograph, 
which  makes  a  permanent 
record  of  the  observation 

upon  a  sheet  of  paper,  — 
FIG.  106.— The  Meridian  Circle  (schematic) 

thus  making  the  observa- 
tion much  more  accurate  as  well  as  easier. 

For  the  description  of  the  Chronograph,  see  General  Astronomy, 
Art.  56,  or  Manual,  Sec.  59. 

418.  The  Meridian  Circle,  or  Transit  Circle.  —  In  many 
respects  this  is  the  fundamental  instrument  of  a  working 
observatory.  It  is  simply  the  transit-instrument  plus  a  finely 
graduated  circle  or  circles  attached  to  the  axis  and  provided 
with  microscopes  for  reading  the  graduation  with  precision. 
In  the  accurate  construction  of  the  pivots  of  the  instru- 
ment and  of  the  circles,  with  their  graduation,  the  utmost 
resources  of  the  mechanical  art  are  taxed.  Fig.  107  shows 


THE  MERIDIAN  CIRCLE 


375 


the  instrument  in  principle.  Fig.  107  represents  the  new 
meridian  circle  of  the  Washington  Observatory  with  its  acces- 
sories. It  has  a  telescope  of  6  inches  aperture  and  circles 
27  inches  in  diameter. 


FIG.  107. — Transit,  or  Meridian,  Circle  in  United  States  Naval  Observatory 

at  Washington 
By  Warner  and  Swasey 

Its  main  purpose  is  to  determine  the  right  ascension  and 
declination  of  objects  as  they  cross  the  meridian.  The 
declination  is  determined  by  measuring  how  many  degrees 


376  APPENDIX 

the  object  is  north  or  south  of  the  celestial  equator  at  the 
moment  of  transit.  The  "  circle-reading "  for  the  equator 
must  first  be  determined  as  a  zero  point;  and  this  is  done  by 
observing  a  star  near  the  pole  and  getting  the  circle-reading  as 
it  crosses  the  meridian  above  the  pole,  and,  twelve  hours  later, 
when  it  crosses  again  below  it.  The  mean  of  these  two  read- 
ings, corrected  for  refraction,  will  be  the  circle-reading  for 
the  pole,  or  the  polar  point,  which  is,  of  course,  just  90°  from 
the  equatorial  zero  point. 

419.  The  Nadir  Point.  —  To  get  the  latitude  of  the  observer 
with  this  instrument  (Sec.  81)  it  is  necessary  also  to  have 
the  nadir  point  as  a  zero,  i.e.,  the  circle-reading  which  corre- 
sponds to  the  vertical   position  of  the  telescope.     This  is 
found  by  pointing  the  telescope  down  towards  a  basin  of 
mercury  beneath  it,  and  setting  it  so  that  the  image  of  the 
east  and  west  wire  in  the  reticle  coincides  with  itself.     Then 
the  telescope  will  be  exactly  vertical.     The  horizontal  point 
is  just  90°  from  the  nadir  point,  and  the  difference  between 
the  (north)  horizontal  point  and  the  polar  point  is  the  latitude 
of  the  observatory. 

Obviously  the  instrument  can  also  be  used  as  a  simple 
transit-instrument  in  connection  with  a  clock,  so  that  (Sec.  99) 
the  observer  can  determine  at  one  observation  both  the  right 
ascension  and  declination  of  any  object  which  is  visible  when 
it  crosses  the  meridian. 

420.  The  Sextant All  the  instruments  so  far  mentioned, 

except  the  chronometer,   require  firmly  fixed  supports,   and 
are,  therefore,  useless  at  sea.     The  sextant  is  the  only  instru- 
ment for  measurement  upon  which  the  mariner  can  rely.     By 
means  of  it  he  can  measure  the  angular  distance  between  any 
two  points  (as,  for  instance,  the  sun  and  the  visible  horizon), 
not  by  pointing  first  on  one  and  afterwards  on  the  other,  but 
by  sighting  them  both  simultaneously  and  in  apparent  coinci- 
dence.    This  observation  can  be  accurately  made  even  if  he 


THE  SEXTANT 


377 


has  no  stable  footing,  but  is  swinging  about  on  the  deck  of  a 
vessel.  Fig.  108  represents  the  instrument.  (For  a  detailed 
description  and  explanation,  see  General  Astronomy,  Arts. 
76-80,  or  Manual,  Sees.  73-75.) 

421.  Use  of  the  Instrument. — The  principal  use  of  the 
instrument  is  in  measuring  the  altitude  of  the  sun.  At  sea, 
an  observer  holding  the  instrument  in  his  right  hand  and 


S 


S' 


FIG.  108.  —  The  Sextant 

keeping  the  plane  of  the  arc  vertical,  looks  directly  towards 
the  visible  horizon  through  the  horizon-glass,  H,  at  the  point 
under  the  sun.  Then  by  moving  the  index,  N,  with  his  left 
hand,  he  inclines  the  index  mirror  upward  until  he  sees  the 
reflected  image  of  the  sun,  and  the  lower  edge  of  this  image  is 
brought  to  touch  the  horizon  line.  The  reading  of  the  gradu- 
ation, after  due  correction  for  refraction,  etc.,  gives  the  sun's 
true  altitude  at  the  moment.  If  the  observation  is  made  very 


378  APPENDIX 

near  noon,  for  the  purpose  of  determining  the  latitude,  it  will 
not  be  necessary  to  read  the  chronometer  at  the  same  time. 
If,  however,  the  observation  is  made  for  the  purpose  of  deter- 
mining the  longitude  (Sec.  427),  the  instant  of  observation,  as 
shown  by  the  chronometer,  must  be  carefully  noted. 

The  skillful  use  of  the  sextant  requires  considerable  dex- 
terity, and  from  the  small  size  of  the  telescope  the  angles 
measured  are  less  precisely  measured  than  with  large  fixed 
instruments;  but  the  portability  of  the  instrument  and  its 
applicability  at  sea  render  it  absolutely  invaluable.  It  was 
invented  by  Godfrey  of  Philadelphia,  in  1730,  but  an  earlier 
design  of  an  instrument  on  the  same  principle  has  since  been 
found  among  the  unpublished  papers  of  Newton. 


MISCELLANEOUS 

Hour- Angle  and  Time  —  Twilight  —  Determination  of  Latitude  —  Ship's  Place 
at  Sea  — Finding  the  Form  of  the  Earth's  Orbit  — The  Ellipse  —  Illustra- 
tions of  Kepler's  Third  Law  — The  Ecfuation  of  Light  and  the  Sun's  Dis- 
tance—Aberration of  Light  — De  1'Isle's  Method  of  getting  the  Solar 
Parallax  from  the  Transit  of  Venus  —  The  Conic  Sections  —  Stellar 
Parallax 

422.  Hour-Angle  and  Time  (supplementary  to  Sees.  89-91). 
—  There  is  another  way  of  looking  at  the  matter  of  time 
which  has  great  advantages.  If  we  face  towards  the  north 
pole  and  consider  the  star  m  (Fig.  109)  as  carried  at  the  end 
of  the  arc  mP  of  the  hour-circle  which  connects  it  to  the  pole, 
we  may  regard  this  arc  as  a  sort  of  clock-hand ;  and  if  we 
produce  it  to  the  celestial  equator  and  mark  off  the  equator 
into  15°-spaces,  or  "hours,"  the  angle  mQP,  or  the  arc  QY, 
will  measure  the  time  which  has  elapsed  since  m  was  on  the 
meridian  PQ.  The  angle  mPQ  is  called  the  hour-angle  of  the 
star  m.  It  is  the  angle  at  the  pole  between  the  meridian  and 
the  hour-circle  which  passes  through  the  body. 


HOUR-ANGLE  AND  TWILIGHT 


379 


Having  now  this  definition  of  the  hour-angle,  we  may 
define  sidereal  time  (Sec.  91)  at  any  moment  as  the  hour-angle 
of  the  vernal  equinox  at  that  moment.  In  the  same  way,  the 
apparent  solar  time  (Sec.  88)  is  the  hour-angle  of  the  sun's 
center ;  the  mean  solar  time  (Sec.  89)  is  the  hour-angle  of  a 
fictitious  sun  which  moves  around  the  heavens  uniformly,  once 
a  year,  in  the  equator,  keeping  its  right  ascension  equal  to 
the  mean  longitude  of  the  real  sun.  For  some  purposes,  as 
in  dealing  with  the  tides, 
it  is  convenient  to  use 
lunar  time,  which  is  sim- 
ply the  hour-angle  of  the 
moon  at  any  moment. 

423.  Twilight  is  caused 
by  the  reflection  of  sunlight 
from  the  upper  portions  of 
the  earth's  atmosphere.  After 
the  sun  has  set,  its  rays  still 
continue  to  shine  through  the 
air  above  the  observer's  head, 
and  twilight  contin  ues  as  long 
as  any  portion  of  this  illu- 
minated air  can  be  seen  from 

where  he  stands.  It  is  considered  to  end  when  stars  of  the  sixth 
magnitude  become  visible  near  the  zenith,  which  does  not  occur 
until  the  sun  is  about  18°  below  the  horizon ;  but  this  is  not  strictly 
the  same  for  all  places. 

The  duration  of  twilight  varies  with  the  season  and  with  the 
observer's  latitude.  In  latitude  40°  it  is  about  ninety  minutes  on 
March  1  and  October  12,  but  more  than  two  hours  at  the  summer 
solstice.  In  latitudes  above  50°,  when  the  days  are  longest,  twilight 
never  quite  disappears,  even  at  midnight,  and  in  latitude  60°  one 
can  read  fair-sized  type  all  night  long.  On  the  mountains  of 
Peru,  on  the  other  hand,  it  is  said  never  to  last  more  than  half 
an  hour. 


FIG.  109.  —  Hour- Angle 


380 


APPENDIX 


424.  Methods  of  determining  Latitude  by  Other  Obser- 
vations than  those  of  Circumpolar  Stars  (supplementary  to 
Sec.  81).  —  To  determine  the  latitude  by  observations  of  a  cir- 
cumpolar  star,  the  observer  must  remain  at  the  same  station 
at  least  twelve  hours.  The  latitude  can  be  determined,  how- 
ever, with  a  good  instrument,  with  almost  equal  precision  by 
observing  the  meridian  altitude,  or  zenith  distance,  of  a  body 
whose  declination  is  accurately  known.  In  Fig.  110  the  circle 
SQPN  is  the  meridian,  Q  and  P  being  respectively  the  equa- 
tor and  the  pole,  and  Z  the  zenith.  QZ  is  evidently  the 
declination  of  the  zenith  (i.e.,  the  distance  of  the  zenith  from 
the  celestial  equator)  and  is  equal  to  PB,  the  latitude  of  the 
observer,  or  height  of  the  pole.  Suppose  now  that  we  observe 
Zs,  i.e.,  the  zenith  distance  of  the  star  s,  south  of  the  zenith, 

as  it  crosses  the  meridian,  and 
that  we  know  Qs,  the  declina- 
tion of  the  star.  Evidently 
QZ  =  Qs  +  sZ  ;  i.e.,  the  latitude 
equals  the  declination  of  the  star 
\N  plus  its  zenith  distance.  If  the 
star  were  at  s',  south  of  the 
equator,  the  same  equation  would 
hold  good  algebraically,  because 
the  declination,  Qs',  is  a  minus  quantity.  If  the  star  were  at 
n,  between  the  zenith  and  the  pole,  we  should  have :  latitude 
equals  the  declination  of  the  star  minus  the  zenith  distance. 

This  is  the  method  actually  used  at  sea  (Sec.  426),  the  sun  being 
the  object  observed. 

There  are  many  other  methods  in  use,  as,  for  instance,  that, 
by  the  zenith  telescope  and  that  by  the  prime-vertical  instru- 
ment, which  are  practically  more  convenient  and  more  accu- 
rate than  either  of  the  two  described,  but  they  are  more 
complicated  and  their  explanation  would  take  us  too  far. 


FIG.  110.  — Determination  of 
Latitude 


MARINE  ASTRONOMY  381 

FINDING   THE   PLACE   OF   A   SHIP 

425.  The  determination  of  the  place  of  a  ship  at  sea  is, 
from  the  economic  point  of  view,  the  most  important  problem 
of  Astronomy.     National  observatories  and  nautical  almanacs 
were    established,  and  are  maintained  principally  to  supply 
the  mariner  with  the  data  needed  to  make  this  determination 
accurately  and  promptly.     The  methods  employed  are  neces- 
sarily such  that  the  required  observations  can  be  made  with 
the  sextant  and  chronometer,  since  fixed  instruments,  like  the 
transit-instrument  and  meridian  circle,  are  obviously  out  of 
the  question  on  board  a  vessel. 

426.  Latitude  at  Sea.  —  This  is  obtained  by  observing  with 
the  sextant  the  sun's  maximum   altitude,  which  is  reached 
when  the  sun  is  crossing  the  meridian. 

Since  at  sea  the  sailor  seldom  knows  beforehand  the  precise 
time  which  will  be  shown  by  his  chronometer  at  noon,  he 
takes  care  not  to  be  too  late,  and  begins  to  measure  the  sun's 
altitude  a  little  before  noon,  repeating  his  observations  every 
minute  or  two.  At  first  the  altitude  will  keep  increasing,  but 
when  noon  comes  the  sun  will  cease  rising,  and  then  begin  to 
descend.  The  observer  uses,  therefore,  the  maximum  altitude 
obtained,  which,  with  due  allowance  for  refraction  and  some 
other  corrections  (for  details,  see  larger  works),  gives  him  the 
true  altitude  of  the  sun's  center.  Taking  this  from  90°,  we 
get  its  zenith  distance. 

Kef  erring  now  to  Fig.  110,  in  which  the  circle  SQZPN  is 
the  meridian,  P  the  pole,  Z  the  zenith,  and  OQ  the  celestial 
equator  seen  edgewise,  we  see  that  PN,  the  altitude  of  the  pole, 
is  necessarily  equal  to  ZQ,  the  distance  from  the  zenith  to  the 
equator.  Now,  from  the  almanac,  we  find  Qs,  the  declination 
of  the  sun  for  the  time  when  the  observations  are  made.1 

1  If  the  sun  happened  to  be  south  of  the  equator  (in  the  winter),  as  at 
s',  we  should  have  ZQ  equals  Zs'—  s'Q. 


382  APPENDIX 

We  have  only  to  add  to  this  Zs,  the  distance  of  the  sun  from 
the  zenith  (i.e.,  90°  —  Ss,  the  observed  altitude  of  the  sun),  to 
obtain  QZ,  which  is  the  observer's  latitude. 

It  is  easy  in  this  way,  with  a  good  sextant,  to  get  the  lati- 
tude within  about  half  a  minute  of  arc,  or,  practically,  about 
half  a  mile,  which  is  quite  sufficiently  accurate  for  nautical 
purposes. 

427.  Determination  of  Local  Time  and  Longitude  at  Sea. 
-  The  usual  method  now  employed  for  the  longitude  depends 
upon  the  chronometer.  This  is  carefully  "  rated  "  in  port ; 
i.e.,  its  error  and  its  daily  gain  or  loss  are  determined  by  com- 
parisons with  an  accurate  clock  for  a  week  or  two,  the  clock 
itself  being  kept  correct  to  Greenwich  time  by  transit  obser- 
vations. By  merely  allowing  for  the  gain  or  loss  since  leaving 
port,  and  adding  this  gain  or  loss  to  the  "error"  (Sec.  417) 
which  the  chronometer  had  when  brought  on  board,  the  sea- 
man at  once  obtains  the  error  of  the  chronometer  on  Green- 
wich time  at  any  moment ;  and  allowing  for  this  error,  he  has 
the  Greenwich  time  itself  with  an  accuracy  which  depends 
only  on  the  constancy  of  the  chronometer's  rate :  it  makes  no 
difference  whether  it  is  gaining  much  or  little,  provided  its 
daily  rate  is  steady. 

He  must  also  determine  his  own  local  time;  and  this  must 
be  done  with  the  sextant,  since,  as  was  said  before,  an  instru- 
ment like  the  transit  cannot  be  used  at  sea.  He  does  it  by 
measuring  the  altitude  of  the  sun,  not  at  or  near  noon,  as  often 
supposed,  but  when  the  sun  is  as  near  due  east  or  west  as  cir- 
cumstances permit.  From  such  an  observation  the  sun's  hour- 
angle,  i.e.,  the  apparent  solar  time  (Sec.  422),  is  easily  found 
by  a  trigonometrical  calculation,  provided  the  ship's  latitude 
is  known.  (For  the  method  of  calculation,  see  General 
Astronomy,  Art.  116,  or  Manual,  Sec.  103.) 

The  longitude  follows  at  once,  being  simply  the  difference 
between  the  Greenwich  time  and  the  local  time. 


FORM  OF  THE  EARTH'S  ORBIT 


383 


In  certain  cases  where  the  chronometers  have  been  for 
some  reason  disturbed,  the  mariner  is  obliged  to  get  his  Green- 
wich time  by  observing  with  a  sextant  the  distance  of  the 
moon  from  some  star  or  planet  near  the  ecliptic,  but  the 
results  thus  obtained  are  comparatively  inaccurate. 

428.  To  find  the  Form  of  the  Earth's  Orbit  (supplementary 
to  Sec.  119).  —  Take  the  point  S  (Fig.  Ill)  for  the  .sun,  and 
draw  through  it  a  line,  OS  °f,  directed  towards  the  vernal 
equinox,  from  which  longitudes  are  measured.  Lay  off  from  S 
lines  indefinite  in  length,  making  angles  with  S°f  equal  to  the 
earth's  longitude  as  seen 
from  the  sun  on  each 
of  the  days  when  the 
observations  are  made 
(earth's  longitude  equals 
sun's  longitude  -f-  180°). 
We  shall  thus  get  a  sort 
of  "spider"  showing  the 
direction  of  the  earth  as 
seen  from  the  sun  on 
each  of  those  days. 

Next,  as  to  the  dis- 
tances. While  the  ap- 
parent diameter  of  the 
sun  does  not  tell  us  its  absolute  distance  from  the  earth,  unless 
we  know  his  diameter  in  miles,  yet  the  changes  in  the  appar- 
ent diameter  do  inform  us  as  to  the  relative  distance  at 
different  times,  since  the  nearer  we  are  to  the  sun,  the  larger 
it  looks.  If,  then,  on  the  legs  of  the  "  spider  "  we  lay  off  dis- 
tances inversely  proportional l  to  the  number  of  seconds  of  arc 
in  the  sun's  measured  diameter  at  each  date,  these  distances 
will  be  proportional  to  the  true  distance  of  the  earth  from  the 

10000" 
ij.e.,  lay  off  Si,  S2,  etc.,  each  equal  to diameter  • 


Fia.  111.  —  Determination  of  the  Form 
of  the  Earth's  Orbit 


384 


APPENDIX 


sun,  and  the  curve  joining  the  points  thus  obtained  will  be  a 
true  map  of  the  earth's  orbit,  though  without  any  scale  of 
miles.  When  the  operation  is  performed  we  find  that  the 
orbit  is  an  ellipse  of  small  eccentricity  with  the  sun  in  one 
of  the  two  foci. 

429.  The  Ellipse,  and  Definitions  relating  to  it  (supplemen- 
tary to  Sees.  119,  120).  —  If  we  drive  two  pins  into  a  board, 
,as  at  F  and  S  in  Fig.  112,  and  put  around  the  pins  a  looped 
thread,  attached  to  the  point  of  a  pencil,  P,  then,  on  carrying 
the  pencil  around,  it  will  mark  out  an  ellipse.     The  pins,  F 

and  S,  are  the  "  foci "  of  the 
ellipse  and  C  is  its  center. 
From  the  manner  in  which 
the  ellipse  is  constructed  it 
\A  is  clear  that  at  any  point,  P, 
on  its  outline,  the  sum  of 
the  two  lines  PS  and  PF  will 
always  be  the  same,  and  equal 

to  the  line  A  A'.     The  length 
FIG.  112.  — The  Ellipse  .  ,_         ...  t.    .         „    _ 

of  the  ellipse,  A  A',  is  called 

its  major  axis,  and  AC  its  semi-major  axis,  which  is  usually 
designated  by  a,  while  the  semi-minor  axis,  BC,  is  lettered  b. 

CS 

The  fraction,  — —  ,  is  called  the  eccentricity  of  the  ellipse  and 
A  C 

determines  the  shape  of  the  oval.  Its  usual  symbol  is  e.  If  e 
is  nearly  unity,  i.e.,  if  CS  is  nearly  equal  to  CA,  the  oval 
will  be  very  narrow  compared  with  its  length ;  but  if  CS  is 
very  small  compared  with  CA,  the  ellipse  will  be  almost  round. 
Taken  together,  a  and  e  determine  the  size  and  form  of  the 
oval.  The  ellipse  is  called  a  "conic  "  because  when  a  cone  is 
cut  across  obliquely  the  section  is  an  ellipse.  (See  Sec.  440.) 

430.  Problems  illustrating  the  "  Harmonic  Law  "  (supplementary 
to  Sec.  220).  —  To  aid  the  student  in  apprehending  the  scope  of 
Kepler's  third  law,  we  give  a  few  examples  of  its  application. 


PROBLEMS  385 

1.  What  would  be  the  period  of  a  planet  having  a  mean  distance 
from  the  sun  of  one  hundred  astronomical  units,  i.e.,  a  distance  a 
hundred  times  that  of  the  earth?  _j_^ 

PMOO»=  I2(year):  X*  ; 
whence  X  (in  years)  =  VlOO3  =  1000  years. 

2.  What  would  be  the  distance  from  the  sun  of  a  planet  having  a 
period  of  125  years  ? 

I2  (year)  :  1252  =  I3  :  Xs  ;  whence  X  =  VI252  =  25  astron.  units. 

3.  What  would  be  the  period  of  a  satellite  revolving  close  to  the 
earth's  surface  ? 

(Moon's  Dist.)3  :  (Dist.  of  Satellite)3  =  (27.3  days)2  :  X2, 
or,  608  :  I3  =  27.32  :  X2  ; 

whence  X  =  27^.  days  =  Od.0587  =  Ih24m.5. 
V603 

4.  How  much  would  an  increase  of  10  per  cent  in  the  earth's 
distance  from  the  sun  lengthen  the  year  ? 


1003  :  HO3  =  (365i)2  :  X*,  whence  X  = 

X  being  the  new  length  of  the  year.  X  is  found  by  computation 
(most  conveniently  by  the  help  of  logarithms)  to  be  421.38  days. 
The  increase  is  56.13  days. 

5.  What  is  the  distance  from  the  sun  of  an  asteroid  with  a  period 
of  3£  years? 

I2  (year)  :  3.52  =  I3  :  Dist.8 

-.-  Dist.  =  V(3.5)2  =  \/12.25  =  2.305  astron.  units. 

431,  The  Equation  of  Light.  —  When  we  observe  a  celestial 
body,  we  see  it  not  as  it  is  at  the  moment  of  observation,  but 
as  and  where  it  was  at  the  moment  when  the  light  which  we 
see  left  it.  If  we  know  its  distance  in  astronomical  units 
and  know  how  long  light  takes  to  traverse  that  unit,  we  can 
at  once  correct  our  observation  by  simply  dating  it  back  to 
the  time  when  the  light  started  from  the  object.  The  neces- 
sary correction  is  called  the  "  equation  of  light"  and  the  time 


386  APPENDIX 

required  by  light  to  traverse  the  astronomical  unit  of  distance 
is  called  the  "  Constant  of  the  Light-Equation  "  (not  quite  500 
seconds,  as  we  shall  see). 

It  was  in  1675  that  Roemer,  the  Danish  astronomer  (the  inventor 
of  the  transit-instrument,  meridian  circle,  and  prime-vertical  instru- 
ment, —  a  man  almost  a  century  in  advance  of  his  day),  found  that 
the  eclipses  of  Jupiter's  satellites  show  a  peculiar  variation  in  their 
times  of  occurrence,  which  he  explained  as  due  to  the  time  taken  by 
light  to  pass  through  space.  His  bold  and  original  suggestion  was 
neglected  for  more  than  fifty  years,  until  long  after  his  death,  when 
Bradley's  discovery  of  aberration  (Sec.  435)  proved  the  correctness 
of  his  views. 

432.  Determination  of  the  Constant  of  the  Equation  of 
Light.  —  Eclipses  of  the  satellites  of  Jupiter  recur  at  intervals 
which  are  really  almost  exactly  equal  (the  perturbations  being 
very  slight),  and  the  interval  can  easily  be  determined  and  the 
times  tabulated.  But  if  we  thus  predict  the  times  of  the 
eclipses  during  a  whole  synodic  period  of  the  planet,  then, 
beginning  at  the  time  of  opposition,  it  is  found  that  as  the 
planet  recedes  from  the  earth  the  eclipses,  as  observed,  fall 
constantly  more  and  more  behindhand  and  by  precisely  the 
same  amount  for  all  four  satellites.  The  difference  between 
the  predicted  and  observed  time  continues  to  increase  until 
the  planet  is  near  conjunction,  when  the  eclipses  are  about 
16m388  later  than  the  prediction.  After  the  conjunction  they 
quicken  their  pace  and  make  up  the  loss,  so  that  when  oppo- 
sition is  reached  once  more  they  are  again  on  time. 

It  is  easy  to  see  from  Fig.  113  that  at  opposition  the  planet 
is  nearer  the  earth  than  at  conjunction  by  just  two  astronom- 
ical units.  At  opposition  the  distance  between  Jupiter  and 
the  earth  is  JA,  while  six  and  a  half  months  later,  at  the 
time  of  Jupiter's  superior  conjunction,  it  is  JB.  The  differ- 
ence between  JA  and  JB  is  just  twice  the  distance  from  S 
to  A. 


THE  EQUATION  OF  LIGHT 


387 


The  whole  apparent  retardation  of  eclipses  between  opposi- 
tion and  conjunction  must  therefore  be  exactly  twice  the  time1 
required  for  light  to  come  from  the  sun  to  the  earth.  In  this 
way  the  "  light-equation  constant "  is  found  to  be  very  nearly 
499  seconds,  or  8  minutes  19  seconds,  with  a  probable  error 
of  perhaps  two  seconds. 

433.  Since  these  eclipses  are  gradual  phenomena,  the  determina- 
tion of  the  exact  moment  of  a  satellite's  disappearance  or  reappear- 
ance is  very  difficult,  and  this 

renders  the  result  somewhat 

uncertain.      Professor   E.    C. 

Pickering  of  Cambridge  has 

proposed  to  utilize  photometric 

observations  for  the  purpose 

of  making  the  determination 

more  precise,  and  two  series 

of  observations  of  this  sort, 

and    for   this   purpose,    have 

been   made    during   recent 

years,  —  one    of    them  in 

Cambridge,  U.S.,  and  the 

other  at  Paris  under  the  direc- 

tion  of  Cornu,  who  devised  a          FJQ  113>  _The  Equation  of  Light 

similar  plan.    The  Cambridge 

results  are  discussed  in  Vol.  LII  of  the  Harvard  Annals. 

Pickering  has  also  applied  photography  to  the  observation  of  these 
eclipses  with  encouraging  success. 

434.  The  Distance  of  the  Sun  determined  by  the  "  Light- 
Equation."  —  Until  1849,  when  Fizeau  first  succeeded  in  actu- 
ally measuring  it,  our  only  knowledge  of  the  velocity  of  light 

1  The  student's  attention  is  specially  directed  to  the  point  that  the 
observations  of  the  eclipses  of  Jupiter's  satellites  give  directly  neither  the 
velocity  of  light  nor  the  distance  of  the  sun  ;  they  give  only  the  time 
required  by  light  to  make  the  journey  from  the  sun.  Many  elementary 
text-books,  especially  the  older  ones,  state  the  case  carelessly. 


388 


APPENDIX 


was  obtained  from  such  observations  of  Jupiter's  satellites. 
By  assuming  as  known  the  earth's  distance  from  the  sun,  the 
velocity  of  light  can  be  obtained  when  we  know  the  time 
occupied  by  light  in  coming  from  the  sun. 

At  present,  however,  the  case  is  reversed.  We  can  deter- 
mine the  velocity  of  light  by  two  independent  experimental 
methods,  and  with  a  surprising  degree  of  accuracy.  Then, 
knowing  this  velocity  and  the  "  light-equation  constant,"  we 
can  deduce  the  distance  of  the  sun.  According  to  the  latest 
determinations  the  velocity  of  light  is  186,330  miles  per 

second.  Multiplying  this 
by  499,  we  get  92,979000 
miles  for  the  sun's  distance. 
(Compare  Sec.  436.) 

435.  Aberration  of 
Light. —The  fact  that 
light  is  not  transmitted 
instantaneously  causes  the 
apparent  displacement  of 
an  object  viewed  from  any 
moving  station,  unless  the 
motion  is  directly  towards 
or  from  that  object.  If  the  motion  of  the  observer  is  not 
rapid,  this  displacement,  or  "  aberration,"  is  insensible ;  but 
the  earth  moves  so  swiftly  in  its  orbit  (18£  miles  per  second) 
that  it  is  easily  observable  in  the  case  of  the  stars.  Astro- 
nomical aberration  may  be  defined,  therefore,  as  the  apparent 
displacement  of  a  heavenly  body  due  to  the  combination  of  the 
orbital  motion  of  the  earth  with  that  of  light  —  the  direction 
in  which  we  have  to  point  our  telescope  in  observing  a  star 
is  not  the  same  as  if  the  earth  were  at  rest. 

We  may  illustrate  this  by  considering  what  would  happen  in  the 
case  of  falling  raindrops.  Suppose  the  observer  standing  with  a 
tube  in  his  hand  while  the  drops  are  falling  straight  down :  if  he 


FIG.  114.  — Aberration 


ABERRATION  389 

wishes  to  have  the  drops  descend  through  the  middle  of  the  tube 
without  touching  the  sides,  he  must  keep  it  vertical  so  long  as  he 
stands  still  ;  but  if  he  advances  in  any  direction  the  drops  will  strike 
the  side  of  the  tube,  and  he  must  thrust  forward  its  upper  end 
(Fig.  114)  by  an  amount  which  equals  the  advance  he  makes  while 
a  drop  is  falling  through  it  ;  i.e.,  he  must  incline  the  tube  forward  at 
an  angle  depending  both  upon  the  velocity  of  the  raindrop  and  the 
swiftness  of  his  own  motion,  so  that  when  the  drop,  which  entered 
the  tube  at  J5,  reaches  A',  the  bottom  of  the  tube  will  be  there  also. 
It  is  true  that  this  illustration  is  not  a  demonstration,  because  light 
does  not  consist  of  particles  coming  towards  us,  but  of  waves  trans- 
mitted through  the  ether  of  space.  But  it  has  been  shown  (though 
the  proof  is  by  no  means  elementary)  that  within  very  narrow  limits 
the  apparent  direction  of  a  wave  is  affected  in  precisely  the  same  way 
as  that  of  a  moving  projectile. 

Observations  on  several  hundred  stars  show  that  a  star  situ- 
ated on  a  line  at  right  angles  to  the  direction  of  the  earth's 
motion  is  thus  apparently  displaced  by  an  angle  of  about  20  ".5. 

This  is  the  so-called  "  CONSTANT  OF  ABERRATION." 

The  Astronomical  Congress  at  Paris  in  1896  adopted  the 
value  20".47,  but  a  series  of  observations  by  Doolittle,  extend- 
ing from  1899  to  1911,  carry  it  up  to  20".525. 

If  the  star  is  in  a  different  part  of  the  sky  its  displacement 
will  be  less,  the  amount  being  easily  calculated  when  the  date 
and  the  star's  position  are  given. 

436.  Determination  of  the  Sun's  Distance  by  Means  of  the 
Aberration  of  Light.  —  The  constant  of  aberration,  a,  and 
the  two  velocities,  that  of  the  earth  in  its  orbit,  u,  and  the 
velocity  of  light,  V,  are  connected  by  the  very  simple  equation 

a  =  206,265  x  |;  whence  it  =  X  V. 


When,  therefore,  we  have  ascertained  the  value  of  a  (20".52) 
from  observations  of  the  stars,  and  of  V  (186,330  miles,  accord- 
ing to  the  most  recent  determinations  by  Michelson  and 


390  APPENDIX 

Newcomb)  by  physical  experiments,  we  can  immediately  find 
u,  the  velocity  of  the  earth  in  her  orbit.  The  circumference  of 
the  earth's  orbit  is  then  found  by  multiplying  this  velocity,  u, 
by  the  number  of  seconds  in  a  sidereal  year  (Sec.  127)  ;  and 
from  this  we  get  the  radius  of  the  orbit,  or  the  earth's  mean 
distance  from  the  sun,  by  dividing  the  circumference  by  2  TT 
(TT  =  3.14159).  Taking  a  =  20".52,  the  mean  distance  of  the 
sun  comes  out  93,104000  miles. 

But  the  uncertainty  of  a  is  probably  as  much  as  0".03,  and 
this  affects  the  distance  proportionally,  say  one  part  in  600, 
or  150,000  miles.  Still,  the  method  is  one  of  the  very  best 
of  all  that  we  possess  for  determining  in  miles  the  value  of 
"the  Astronomical  Unit." 

437.  De  1'Isle's  Method  of  determining  the  Sun's  Parallax 
by  a  Transit  of  Venus.  —  We  have  thus  (Sees.  434  and  436) 
two  methods  by  which  the  mean  distance  of  the  sun  from  the 


FIG.  115.  — Transit  of  Venus 

earth  can  be  determined.  They  both  depend  upon  a  knowl- 
edge of  the  velocity  of  light,  and,  of  course,  were  unavailable 
before  1849,  when  Fizeau  first  succeeded  in  actually  measuring 
it.  Before  that  time  it  was  necessary  to  rely  entirely  upon 
observations  of  either  Mars  or  Venus,  made  at  times  when 
they  come  specially  near  us. 

Most  of  the  methods  of  getting  the  sun's  parallax  and  dis- 
tance from  such  observations  depend  upon  our  having  a  pre- 
vious knowledge  of  the  relative  distances  of  the  planets  from 
the  sun.  These  relative  distances  were  ascertained  centuries 


TRANSITS  OF  VENUS  391 

ago.  Copernicus  knew  them  nearly  as  accurately  as  we  have 
them  now ;  but  since  we  have  not  explained  in  this  book  how 
they  are  found  (the  explanation  involves  a  little  Trigonom- 
etry), we  limit  ourselves  to  giving  here  a  single  very  simple 
method,  which  requires  a  previous  knowledge  not  of  the  rela- 
tive distances  of  Venus  and  the  earth  from  the  sun,  but  only 
of  the  synodic  period  of  the  planet  (Sec.  228),  i.e.,  the  time  in 
which  she  gains  one  entire  revolution  upon  the  earth.  This 
is  almost  exactly  584  days  (583.971),  as  has  been  known  from 
remote  antiquity. 

Fig.  115  represents  things  at  a  transit  of  Venus  as  they 
would  be  seen  by  one  looking  down  from  an  infinitely  distant 
point  above  the  earth's  north  pole. 
As    seen   from   the    earth   itself, 
Venus  would  appear  to  cross  the 
sun,  striking  the  disk  on  the  east    . 
side  and  moving  straight  across  to 
the  west,  making  four  "  contacts  " 
with  the  edge  of  the  sun,  as  shown 
in  Fig.  116. 

438.   Suppose,  now,  that  two 
observers,   E   and   W   (Fig.   115),   FlG<116._Contact8inaTransit 
are  stationed  opposite  each  other  of  Venus 

and  near  the  earth's  equator. 

E  will  see  Venus  strike  the  sun's  disk  before  W  does,  and  if 
they  both  observe  the  moment  of  contact  in  Greenwich  time, 
the  difference  between  their  records  will  be  the  time  it  takes 
Venus  to  move  over  the  arc  from  V\  to  F2.  From  the  figure 
it  is  clear  that  the  angle  V[DV^  is  the  same  as  EDW,  the 
earth's  apparent  diameter  seen  from  the  sun,  and  this  is  at  once 
known  when  we  have  the  time  from  Vl  to  F2. 

Since  Venus  gains  one  revolution  in  584  days,  in  one  day 
she  will  gain  ^¥  of  a  revolution,  or  37'  (very  nearly),  and 
this  will  make  her  gain  1".54  in  one  minute.  Now  it  is  found 


392 


APPENDIX 


that  the  difference  between  the  moments  of  contact  at  two 
stations  situated  like  E  and  W  is  about  Hm258,  and  hence 
that  the  diameter  of  the  earth,  as  seen  from  the  sun,  is  17".6, 
or  the  sun's  horizontal  parallax  (Sec.  139)  is  8".8  ;  from  which 
its  distance  is  easily  found  (Sec.  140). 

The  reader  will  see  that  the  two  observers  must  know  their 
longitudes  accurately  in  order  to  be  sure  of  the  correct  Green- 
wich time.  Moreover,  the  two  stations  can  never  be  quite 

exactly  opposite 
each  other,  but 
stations  a  little 
nearer  together 
must  be  taken 
and  proper  al- 
lowances made. 
Finally,  we  are 
3  very  sorry  to 
add  that  the 
necessary  obser- 
vations of  the 
moment  when 
Venus  reaches 
the  edge  of  the 
sun's  disk  can- 
not be  made 
with  the  accu- 


FIQ.  117.— Ellipse,  Parabola,  and  Hyperbola 


racy  which  is  desirable,  owing  to  the  effect  of  the  planet's 
atmosphere  (see  Sec.  248) ;  so  that  practically  the  method 
is  less  accurate  than  might  be  hoped.  (For  further  details, 
see  General  Astronomy,  Chap.  XVI.) 

439.   The  Parabola  (supplementary  to  Sees.   292-298).- 
This  differs  from  the  ellipse  in  never  coming  around  into  itself. 
In  Fig.  117,  the  curves  PAlt  PA2,  and  PA8  are  ellipses  of  dif- 
ferent length,  all  having  S  at  one  of  their  foci,  but  having  Flt 


THE  CONICS 


393 


F2,  and  F8  at  the  other.    The  first  and  smallest  of  the  ellipses 
is  nearly  circular  and  shaped  about  like  the  orbit  of  Mercury, 
the  two  foci  S  and  Fl  being  pretty  near  together ;  the  next  is 
more  eccentric  than  the  orbit 
of  any  asteroid ;  and  the  third 
still  more  so,  about  like  the 
orbit  of  Halley's  comet.   Now, 
if  we  imagine  the  point  F  car- 
ried farther  and  farther  to  the 
right   the   ellipse   will   grow 
larger  and  longer,  until  when 
F  is  infinitely  far  away  the 
curve  will  become  a  parabola. 

Of  course  if  the  point  F  is 
very  distant,  even  if  not  infi- 
nitely so,  the  part  of  the  curve 
near  S  will  agree  with  the  parab- 
ola so  closely  that  no  one  could 
distinguish  between  them. 

All  ellipses  that  have  S  for 
the  focus  and  P  for  the  peri- 
helion lie  inside  of  the  parab- 
ola,  while  another  set  of 
conic  curves  called  hyperbolas, 
with  the  same  focus  and  peri- 
helion, lie  entirely  outside  of 
it,  which  is,  so  to  speak,  a  sort 
of  boundary  or  division  line 
between  the  ellipses  and 
hyperbolas  which  have  this 
focus  and  perihelion. 

440.  The  Conic  Sections.  —  The  way  in  which  these  curves 
—  the  ellipse,  parabola,  and  hyperbola  —  are  formed  by  sec- 
tions of  the  cone  is  shown  by  Fig.  118. 


FIG.  118.  —  The  Conies 


894  APPENDIX 

(a)  If  the  cone  be  cut  by  a  plane  which  makes  with  its 
axis,  VC,  an  angle  greater  than  BVC,  the  plane  of  the  section 
will  cut  completely  across  the  cone  and  the  section  EF  will 
be  an  ellipse,  which  will  vary  in  shape  and  size  according  to 
the  position  of  the  plane.     The  circle  is  simply  a  special  case 
when  the  cutting  plane  is  perpendicular  to  the  axis,  as  NM. 

(b)  When  the  cutting  plane  makes  with  the  axis  an  angle 
less  than  BVC  (the  semi-angle  of  the  cone),  it  plunges  contin- 
ually deeper  and  deeper  into  the  cone  and  never  comes  out  on 
the  other  side  (the  cone  is  supposed  to  be  indefinitely  pro- 
longed).    The  section  in  this  case  is  an  hyperbola,  GHK.     If 
the  plane  of  the  section  be  produced  upward,  however,  it 
encounters  the  "  cone  produced,"  cutting  out  from  it  a  second 
hyperbola,  G'H'K',  precisely  like  the  original  one,  but  turned 
in  the  opposite  direction. 

The  axis  of  the  hyperbola  is  always  reckoned  as  negative, 
lying  outside  of  the  curve  itself ;  in  the  figure,  it  is  the  line 
HH'.  The  center  of  the  hyperbola  is  the  middle  point  of  this 
axis,  a  point  also  outside  of  the  curve. 

(c)  When  the  angle  made  by  the  cutting  plane  with  the 
axis  is  exactly  equal  to  the  cone's  semi-angle,  the  plane  will 
be  parallel  to  the  side  of  the  cone,  and  we  then  get  the  special 
case  of  the  parabola,  RPO,  which  forms  a  partition,  so  to 
speak,  between  the  infinite  variety  of  ellipses  and  hyperbolas 
which  can  be  cut  from  a  given  cone.     All  parabolas  are  of  the 
same  shape,  just  as  all  circles  are,  differing  only  in  size.     The 
fact  is  by  no  means  self-evident  and  we  cannot  stop  to  prove 
it,  but  it  is  true. 

441.  Determination  of  the  Parallax  of  a  Star  (supple- 
mentary to  Sec.  343).  —  The  determination  of  the  parallax  of 
stars  had  been  attempted  over  and  over  again  from  the  time  of 
Tycho  Brahe  down,  but  without  success  until,  in  1838,  Bessel 
at  last  demonstrated  and  measured  the  parallax  of  61  Cygni ; 
and  the  next  year  Henderson,  of  the  Cape  of  Good  Hope, 


STELLAR  PARALLAX  395 

determined  that  of  Alpha  Centauri.  The  operation  of  measur- 
ing the  parallax  of  a  star  is,  on  the  whole,  the  most  delicate 
in  the  whole  range  of  practical  Astronomy.  Two  methods  have 
been  used  so  far,  known  as  the  absolute  and  the  differential. 

442.  The  Absolute  Method  consists  in  making  the  most 
scrupulously  precise  observations  of  the  star's  right  ascension 
and  declination  with  the  meridian  circle  at  different  times 
through  the  course  of  an  entire  year,  applying  rigidly  all 
known  corrections  (for  precession,  aberration,  proper  motion, 
etc.),  and  then  examining  the  deduced  positions.     If  the  star 
is  without  parallax,  these  positions  will  all  agree.     If  the  star 
has  a  sensible  parallax,  they  will  show,  on  the  other  hand, 
when  plotted  on  a  chart,  an  apparent  annual  orbital  motion  of 
the  star  in  a  little  ellipse,  the  major  axis  of  which  is  twice  the 
star's  annual  parallax,  as  can  easily  be  shown. 

Theoretically,  the  method  is  perfect ;  practically,  it  seldom 
gives  satisfactory  results,  because  the  annual  changes  of  tem- 
perature and  moisture  disturb  the  instrument  in  such  a  way 
that  the  instrumental  errors  intertwine  themselves  with  the 
parallax  of  a  star  in  a  manner  that  defies  disentanglement. 
No  process  of  multiplying  observations  and  taking  averages 
helps  the  matter  very  much,  because  the  instrumental  errors 
are  themselves  periodic  annually,  just  as  is  the  parallax ;  still, 
in  a  few  cases  the  method  has  proved  successful,  as  in  the 
case  of  Alpha  Centauri,  above  cited. 

443.  The  Differential  Method.  —  This,  the  method  which 
has  principally  proved  successful  thus  far,  consists  in  meas- 
uring the  annual  displacement  of  the  star  whose  parallax  we 
are  seeking,  with  respect  to  other  small  stars  near  it  in  appar- 
ent position  (i.e.,  within  a  few  minutes  of  arc),  but  presumably 
so  far  beyond  as  to  have  no  sensible  parallax  of  their  own. 

If,  for  instance,  the  observer  notes  the  apparent  place  of  an 
object  at  no  great  distance  from  him  with  reference  to  the 
trees  on  a  distant  hillside,  and  then  moves  a  few  feet  one  way 


396  APPENDIX 

or  the  other,  he  will  see  that  the  nearer  object  shifts  its  posi- 
tion with  reference  to  the  trees.  In  the  same  way,  on  account 
of  the  earth's  orbital  motion,  those  stars  which  are  very  near 
the  earth  appear  every  year  to  shift  slightly  backwards  and 
forwards  with  respect  to  those  that  are  far  beyond  them ;  and 
by  measuring  the  amount  of  this  shift  it  is  possible  to  deduce 
approximately  the  parallax  and  distance  of  the  nearer  stars. 

We  say  approximately,  because  the  shift  thus  measured  is 
not  really  the  whole  parallax  of  the  nearer  star,  but  only 
the  difference  between  that  parallax  and  the  parallax  of  the 
remote  objects  with  which  it  is  compared  ;  so  that  observa- 
tions, if  accurately  made,  will  always  give  us  for  the  nearer 
star  a  parallax  too  small,  if  anything,  —  never  too  large  ;  and, 
as  a  consequence,  the  distance  of  the  nearer  star  determined 
in  this  way  will  come  out  a  little  too  large,  and  never  too 
small. 

444.  The  necessary  measurements,  if  the  comparison  stars 
are  within  a  minute  or  two  of  arc,  may  be  made  with  the  filar 
micrometer  (Sec.  415) ;  but  if  the  distance  exceeds  a  few  min- 
utes, we  must  resort  to  the  "  heliometer  "  (see  General  Astron- 
omy, Art.  677)  with  which  Bessel  first  succeeded  ;  or-  we  may 
employ  photography,  which  the  late  Professor  Pritchard  at 
Oxford  and  others  still  more  recently  have  done  with  con- 
siderable success. 

On  the  whole,  the  differential  method,  notwithstanding  the 
fundamental  objection  to  it  that  it  never  gives  us  the  entire 
parallax  of  the  star,  is  at  present  more  trustworthy  than  the 
other. 

It  is  obviously  necessary  to  choose  for  observation  by  either 
method  those  stars  that  are  presumably  near  us.  The  most 
important  indication  of  the  nearness  of  a  star  is  a  large  proper 
motion;  brightness,  also,  is  of  course  confirmatory.  Still, 
neither  of  these  indications  is  certain.  A  star  which  happens 
to  be  moving  directly  towards  or  from  us  shows  no  proper 


STELLAR  PARALLAX  397 

motion  at  all,  however  near  it  may  be  ;  and  the  faint  stars 
are  so  very  much  more  numerous  than  the  brighter  ones  that 
among  their  millions  it  is  quite  likely  that  we  shall  ultimately 
find  individuals  which  are  even  nearer  than  Alpha  Centauri. 

445.  Spectroscopic  Method.  —  In  time  it  will  be  possible  to 
determine  the  distance  of  certain  binary  stars  by  the  help  of 
the  spectroscope.  The  velocity  of  one  or  both  of  the  two 
stars  "in  the  line  of  sight"  can  be  measured  by  the  spectro- 
scope at  different  parts  of  the  star's  orbit,  and  this  will  enable 
us  to  compute  the  size  of  the  orbit  in  miles  when  we  know  its 
period  and  its  inclination  to  the  line  of  sight ;  at  the  same 
time  the  micrometer  measures  will  give  its  angular  dimen- 
sions, and  from  these  data  the  distance  can  be  found.  It  will 
probably  be  many  years,  however,  before  many  results  can 
be  obtained  in  this  way,  because  the  periods  of  most  of  the 
binaries  are  very  long. 

Wright,  of  the  Lick  Observatory,  tested  the  method  in 
1905  upon  Alpha  Centauri,  using  the  spectroscopic  observa- 
tions of  the  star  made  by  him  in  South  America.  He  obtained 
a  parallax  practically  identical  with  that  deduced  from  the 
older  methods. 

There  are  also  several  indirect  methods  of  finding  the  dis- 
tances of  stars.  One  of  these  is  especially  important  because 
it  may  be  applied  to  those  very  far  away.  It  has  been  found 
that  there  is  a  definite  relation  between  the  intensity  of  certain 
lines  in  the  spectrum  of  a  star  and  its  so-called  "  absolute 
magnitude."  (By  this  we  mean  its  magnitude  if  it  were  at  a 
certain  standard  distance  from  the  earth.)  Knowing  the  bright- 
ness of  the  star  as  we  really  see  it,  and  what  its  brightness 
would  be  if  it  were  at  a  given  distance,  we  can  find  its  actual 
distance  from  us. 


SUGGESTIVE  QUESTIONS 

FOR   USE   IN   REVIEWS 


To  many  of  these  questions  direct  answers  will  not  be 
found  in  the  book  ;  but  the  principles  upon  which  the  answers 
depend  have  been  given  and  the  student  will  have  to  use  his 
own  thinking  in  order  to  make  the  proper  application. 

1.  What  point  in  the  celestial  sphere  has  both  its  right  ascen- 
sion and  declination  zero? 

2.  What  angle  does  the  (celestial)  equator  make  with  the  hori- 
zon at  this  place  ? 

3.  Name  the  (fourteen)  principal  points  in  the  celestial  sphere 
(zenith,  etc.). 

4.  What  important  circles  in  the  heavens  have  no  correlatives 
on  the  surface  of  the  earth  ? 

5.  What  constellation  of  the  zodiac  rises  at  sunset  to-day,  and 
which  one  is  then  on  the  meridian  ?     (Use  the  star-maps.) 

6.  If  Vega  comes  to  the  meridian  at  8  o'clock  to-night,  at  what 
time  (approximately)  will  it  transit  eight  days  hence  ? 

7.  What  bright  stars  can  I  observe  on  the  meridian  between 
4  and  5  P.M.,  in  the  middle  of  August  ?     (See  star -maps.) 

8.  At  what  time  of  the  year  will  Sirius  be  on  the  meridian  at 
midnight  ? 

9.  The  declination  of  Vega  is  38°  4 1/;  does  it  pass  the  meridian 
north  of  your  zenith,  or  south  of  it? 

10.  What  are  the  right  ascension  and  declination  of  the  north 
pole  of  the  ecliptic  ? 

11.  What  are  the  longitude  and  latitude  (celestial)  of  the  north 
celestial  pole  (the  one  near  the  Pole-star)  ? 

12.  Can  the  sun  ever  be  directly  overhead  where  you  live  ?     If 
not,  why  not  ? 

13.  What  is  the  zenith  distance  of  the  sun  at  noon  on  June  22 
in  New  York  City  (lat.  40°  42')  ? 

14.  What  are  the  greatest  and  least  angles  made  at  New  York 
by  the  ecliptic  with  the  horizon  at  their  point  of  intersection  ?     Why 
does  the  angle  vary  ? 


SUGGESTIVE  QUESTIONS  399 

15.  If  the  obliquity  of  the  ecliptic  were  30°,  how  wide  would  the 
temperate  zone  be  ?     How  wide  if  the  obliquity  were  50°  ?     What 
must  the  obliquity  be  to  make  the  two  temperate  zones  each  as  wide 
as  the  torrid  zone  ? 

16.  Does  the  equinox  always  occur  on  the  same  days  of  March  and 
September  ?     If  not,  why  not ;  and  how  much  can  the  date  vary  ? 

17.  Was  the  sun's  declination  at  noon  on  March  10,  1900,  pre- 
cisely the  same  as  on  the  same  date  in  1903? 

18.  In  what  season  of  the  year  is  New  Year's  Day  in  Chili  ? 

19.  When  the  sun  is  in  the  constellation  Taurus,  in  what  sign  of 
the  zodiac  is  he  ? 

20.  In  what  constellation  is  the  sun  when  he  is  vertically  over  the 
tropic  of  Cancer  ?     Near  what  star  ?     (See  star-map.) 

21.  When  are  day  and  night  most  unequal  ? 

22.  In  what  part  of  the  earth  are  the  days  longest  on  March  20  ? 
On  June  20  ?     On  December  20  ? 

23.  Why  is  it  warmest  in  the  United  States  when  the  earth  is 
farthest  from  the  sun  ? 

24.  What  was  the  Russian  date  corresponding  to  Feb.  28,  1900, 
of  our  calendar  ?     To  May  28  ? 

25.  Why  are  the  intervals  from  sunrise  to  noon  and  from  noon  to 
sunset  usually  unequal  as  given  in  the  almanac  ?     (For  example,  see 
Feb.  20  and  Nov.  20.) 

26.  If  the  earth  were  to  shrink  to  half  its  present  diameter,  what 
would  be  its  mean  density  ? 

27.  Is  it  absolutely  necessary,  as  often  stated,  to  know  the  diam- 
eter of  the  earth  in  order  to  find  the  distance  of  the  sun  from  the 
earth  ? 

28.  How  will  a  projectile  fired  horizontally  on  .the  earth  deviate 
from  the  line  it  would  follow  if  the  earth  did  not  rotate  on  its  axis? 

29.  If  the  earth  were  to  contract  in  diameter,  how  would  the 
weight  of  bodies  on  its  surface  be  affected  ? 

30.  What  keeps  up  the  speed  of  the  earth  in  its  motion  around 
the  sun  ? 

31.  Why  is  the  sidereal  month  shorter  than  the  synodic  ? 

32.  Does  the  moon  rise  every  day  of  the  month  ? 

33.  If  the  moon  rises  at  Hh45m  Tuesday  night,  when  will  it  rise 
next? 

34.  How   many  times   does   the   moon   turn  on   its   axis  in   a 
year  ? 

35.  What  determines  the  direction  of  the  horns  of  the  moon? 

36.  Does  the  earth  rise  and  set  for  an  observer  on  the  moon  ?     If 
so,  at  what  intervals  ? 

37.  How  do  we  know  that  the  moon  is  not  self-luminous  ? 

38.  How  do  we  know  that  there  is  no  water  on  the  moon? 


400  APPENDIX 

39.  How  much  information  does  the  spectroscope  give  us  about 
the  moon  ? 

40.  What  conditions  must  concur  to  produce  a  lunar  eclipse  ? 

41.  Can  an  eclipse  of  the  moon  occur  in  the  daytime  ? 

42.  Why  can  there  not  be  an  annular  eclipse  of  the  moon  ? 

43.  Which  are  most  frequent  at  New  York,  solar  eclipses  or  lunar  ? 

44.  Can  an  occultation  of  Venus  by  the  moon  occur  during  a" 
lunar  eclipse  ?     Would  an  occultation  of  Jupiter  be  possible  under 
the  same  circumstances? 

45.  Which  of  the  heavenly  bodies  are  not  self-luminous? 

46.  When  is  a  planet  an  evening  star  ? 

47.  What  planets  have  synodic  periods  longer  than  their  sidereal 
periods  ? 

48.  When  a  planet  is  at  its  least  distance  from  the  earth,  what  is 
its  apparent  motion  in  right  ascension  ? 

49.  A  planet  is  seen  120°  distant  from  the  sun;  is  it  an  inferior 
or  a  superior  planet  ? 

50.  Can  there  be  a  transit  of  Mars  across  the  sun's  disk  ? 

51.  When  Jupiter  is  visible  in  the  evening,  do  the  shadows  of  the 
satellites  precede  or  follow  the  satellites  themselves  as  they  cross  the 
planet's  disk? 

52.  What  would  be  the  length  of  the  month  if  the  moon  were 
four  times  as  far  away  as  now  ?     (Apply  Kepler's  third  law.) 

53.  What  is  the  distance  from  the  sun  of  an  asteroid  which  has  a 
period  of  eight  years,?     (Kepler's  third  law.) 

54.  Upon   what   circumstances   does   the   apparent  length  of   a 
comet's  tail  depend  ? 

55.  How  can  the  distance  of  a  meteor  from  the  observer,  and  its 
height  above  the  earth,  be  determined  ? 

56.  What  heavenly  bodies  are  not  included  in  the  solar  system? 

57.  How  do  we  know  that  stars  are  suns?     How  much  is  meant 
by  the  assertion  that  they  are  ? 

58.  Suppose  that  in  attempting  to  measure  the  parallax  of  a  bright 
star  by  the  differential  method  (Sec.  443)  it  should  turn  out  that  the 
small  star  taken  as  the  point  to  measure  from,  and  supposed  to  be  far 
beyond  the  bright  one,  should  really  prove  to  be  nearer.     How  would 
the  measures  show  the  fact  ? 

59.  If  Alpha  Centauri  were  to  travel  straight  towards  the  sun 
with  a  uniform  velocity  equal  to  that  of  the  earth  in  its  orbit,  how 
long  would  the  journey  take,  on  the  assumption  that  the  star's  parallax 
isO".75? 

60.  If  Altair  were  ten  times  as  distant  from  us,  what  would  be 
its  apparent  "  magnitude  "  ?     What,  if  it  were  a  thousand  times  as 
remote  ?     (See  Sees.  346,  347  ;  and  remember  that  the   apparent 
brightness  varies  inversely  with  the  square  of  the  distance.) 


TABLES   OF  ASTRONOMICAL   DATA 

TABLE   I  — ASTRONOMICAL   CONSTANTS 

TIME    CONSTANTS 

The  sidereal  day       =  23h56m48.090  of  mean  solar  time. 

The  mean  solar  day  =  24h3m568.5£6  of  sidereal  time. 

To  reduce  a  time-interval  expressed  in  units  of  mean  solar  time  to 
units  of  sidereal  time,  multiply  by  1.00273791 ;  log.  of  0.00273791 
=  [7.4374191]. 

To  reduce  a  time-interval  expressed  in  units  of  sidereal  time  to 
units  of  mean  solar  time,  multiply  by  0.99726957  =  (1  -  0.00273043); 
log.  0.00273043  =  [7.4362316]. 

Tropical  year  (Leverrier,  reduced  to  1900)     .  365d  5h48m458.51. 

Sidereal  year  "  «  »          .  365    6    9-8.97. 

Anomalistic  year     «  «  «  365     6  13   48 .09. 

Mean  synodical  month  (new  moon  to  new)     .     29d12h44m  28.864. 

Sidereal  month  .  .         .         .         .     : ...     27    7  43    11 .545. 

Tropical  month  (equinox  to  equinox)     .         .     27     7  43      4  .68. 

Anomalistic  month  (perigee  to  perigee)          .     27  13  18    37  .44. 

Nodical  month  (node  to  node)        .         .         .     27    5     5   35  .81. 


Obliquity  of  the  ecliptic  (Newcomb), 

23°  27'  8".26  -  0".468  (t  -  1900). 

Constant  of  precession  (Newcomb), 

50".248  +  0.000222  (t  -  1900). 

Constant  of  nutation  (Peters),  9".223. 

Constant  of  aberration  (Nyren),  20".492  ;  (Chandler),  20".521. 


Equatorial  semi-diameter  of  the  earth  (Clarke's  spheroid  of  1878), 

20,926202  feet  =  6,378190  meters  =  3963.296  miles. 
Polar  semi-diameter, 

'20,854895  feet  =  6,356456  meters  =  3949.790  miles. 
Ellipticity,  or  polar  compression  (Clarke),  293\46;  (Harkness), 

401 


402 


APPENDIX 


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APPENDIX 


TABLE  IV— THE  PRINCIPAL  VARIABLE  STARS 

A  selection  from  S.  C.  Chandler's  catalogue  of  variable  stars,  containing  such  as, 
at  the  maximum,  are  easily  visible  to  the  naked  eye,  have  a  range  of  variation 
exceeding  half  a  magnitude,  and  can  be  seen  in  the  United  States. 


No. 

Name 

Place,  1900 

Range  of 
Variation 

Period  (days) 

Remarks 

a 

S 

1 
2 
3 

R  Andromedse 
o  Ceti    .    .    t. 
p  Persei     .    . 

0  18.8 
2  14.3 
2  58.7 

+  38°  1' 
-  3  26 

+  38  27 

5.6tol3 
1.7  to  9.5 
3.4  to  4.2 

410.7 
331.6 
33? 

(Mira.     Varia- 
{  tions  in  length 
(  of  period 

4 
5 
6 

ft  Persei     .    . 
X  Tauri  .    .    . 
e  Aurigae  .    . 

3    1.6 
3  55.1 

454.8 

+  40  34 

+  12  12 
+  43  41 

2.3  to  3.5 
3.4  to  4.2 
3    to  4.5 

2*  20h  48»>  55S.43 
3d  221*  52»  12* 
Irregular 

(  Algol.      Period 
(  now  shortening 
(  Algol  type,  but 
\  irregular 

7 

a  Orionis   .    . 

549.7 

+   7  23 

0.7  to  1.5 

Irregular 

8 

>j  Geminorum 

6    8.8 

+  22  32 

3.2  to  4.2 

231.4 

9 

£  Geminorum 

658.2 

+  20  43 

3.7  to  4.5 

IQd     3h  41m  3QS.6 

10 

R  Canis  Maj.  . 

7  14.9 

-16  12 

5.9  to  6.7 

Id    3h  i5m  46s 

Algol  type 

11 

R  Leonis    .    . 

9  42.2 

+  11  54 

5.2  to  10 

312.8 

12 

UHydrae    .    . 

10  32.6 

-12  52 

4.5  to  6.3 

194.65 

13 

RHydrae    .    . 

13  24.2 

—22  46 

3.5  to  5.5 

425.15 

Period  short'ing 

14 

8  Librae      .    . 

14  55.6 

-87 

5.0  to  6.2 

24    7h  51m  22».8 

Algol  type 

15 

R  Coronae  .    . 

15  44.4 

+  28  28 

5.8tol3 

Irregular 

16 

RSerpentis    . 

15  46.1 

+  15  26 

5.  6  to  13 

357.0 

17 

a  Herculis 

17  10.1 

+  14  30 

3.1  to  3.9 

Two  or  three  mon 

the,  but  very  irreg. 

18 

U  Ophiuchi    . 

17  11.5 

+   1   19 

6.0  to  6.7 

20»>    7°>  42^.56 

19 

XSagittarii    . 

17  41.3 

-27  48 

4    to  6 

7d    0^  17m  57" 

20 

WSagittarii    . 

1758.6 

-29  35 

5    to  6.5 

7d  14h  16m  133 

21 
22 
23 

R  Scuti  .    .    . 
0  Lyrae  .    .    . 
X  Cygni      .     . 

18  42.1 
18  46.4 
19  46.7 

-   5  49 
+  33  15 
+  32  40 

4.7  to  9 
3.4  to  4.5 
4.0  to  13.5 

71.10 

12*  21*  47°>  23'.  72 
406.045 

(Secondary  mini- 
j  mum  about  mid- 
Period  length'ng 

24 

ij  Aquilae  .    . 

19  47.4 

+   0  45 

3.5  to  4.7 

7d      4h   Urn  593 

25 

S  Sagittae  .     . 

19  51.4 

+  16  22 

5.  6  to  6.4 

gd    gh  urn  48s.5 

26 

T  Vulpeculae  . 

2047.2 

+  27  52 

5.5  to  6.5 

4*  10"  27»  50».4 

27 

TCephei    .    . 

21    8.2 

+  68     5 

5.6  to  9.9 

387 

28 

/u.  Cephei    .    . 

21  40.4 

+  58  19 

4    to  5 

430? 

29 

6  Cephei    .    . 

22  25.4 

+  57  54 

3.7  to  4.9 

5d    g*  47-°  39».3 

30 

/3  Pegasi    .     . 

2258.9 

+  27  32 

2.2  to  2.7 

Irregular 

31 

R  Cassiopeiae  . 

2353.3 

+  50  50 

4.8  to  12 

429.5 

ASTRONOMICAL  DATA 


405 


TABLE   V  — PROPER   MOTIONS  AND  PARALLAXES 
(KAPTEYN,  1901) 


No. 

Name 

Mag. 

Proper 
Motion 

Annual 
Parallax 

Distance 
(light-years) 

1 

a  Centauri 

0.7 

3"  67 

0"  76 

4  3 

2 

LI  21158 

75 

4  75 

047 

69 

3 

61  Cveni 

6.1 

5  16 

041 

80 

4 

Sirius     

—  1.4 

1  31 

038 

8  6 

5 

4  9 

0  16 

032 

10  2 

6 

7 

C.  Z.,V.,243  
Procyon 

8.5 
0  7 

8.70 
1  25 

0.32? 
0  31 

10.2 
10  5 

8 
9 

Groombridge,  34     .... 
Lacaille  9352 

7.9 
7.1 

2.80 
7  00 

0.30 
0  29 

10.9 
11  1 

10 

e  Indi      .             ... 

4.8 

4  68 

028 

11  6 

11 
12 

Arg.-Oeltzen,  17415     .    .    . 
LI.  21258     

9.0 
8.5 

1.27 
440 

0.25 
0.24 

13.1 
13  6 

13 
14 

15 

a  Aquilse  (Altair)    .... 
10  Ursae  Major  is     .... 
•>j  Cassiopeiae 

1.0 
4.2 
3  8 

0.65 
0.50 
1  20 

0.24 
0.20 
0.19 

13.6 
16.3 
17  2 

16 
17 

Arg.-Oeltzen,  10603     .     .    . 
e  Eridani    ....         .    . 

7.0 
4.4 

1.43 
3  03 

0.18 
0.16 

18.1 
204 

18 

a  Lyra?  (Vega)    ..... 

0.4 

036 

0.15 

21.7 

19 

Groombridge,  1830  .     .     .    . 

6.6 

7.05 

0.15? 

21.7 

20 

Polaris 

2  1 

0"  045 

0".074 

44± 

The  above  contains  with  a  single  intentional  exception,  one  interpolation  (No.  6), 
and  the  addition  of  Polaris,  all  the  stars  on  Kapteyn's  list  having  parallaxes  exceed- 
ing 0".14.  There  are  about  as  many  more  on  his  list  with  parallaxes  ranging 
between  CK'.IO  and  0".14. 


THE   GREEK  ALPHABET 


Letters 

Name 

Letters 

Name 

Letters 

Name 

A,  a, 

Alpha. 

I,  i, 

Iota. 

P,  p,  g, 

Rho. 

B,  A 

Beta. 

K,  K, 

Kappa. 

S,  o-,  s, 

Sigma. 

r,y, 

Gamma. 

A,  A, 

Lambda. 

T,r, 

Tau. 

A,  8, 

Delta. 

M,  /*, 

Mu. 

Y,  v, 

Upsilon 

E,  e, 

Epsilon. 

N,v, 

Nu. 

^,  <#>, 

Phi. 

z,  £, 

Zeta. 

E,  |, 

Xi. 

X,  x» 

Chi. 

H,  77, 

Eta. 

O,  o, 

Omicron. 

*,  ^ 

Psi. 

@,  0,  t),  Theta. 


n,  IT,  5>,  Pi. 


Omega. 


MISCELLANEOUS   SYMBOLS 


A.R,.,  or  a,  Right  Ascension. 
Decl.,  or  8,  Declination.. 
X,  Longitude  (Celestial). 
ft  Latitude  (Celestial). 
<£,  Latitude  (Terrestrial). 
a),  Angle  between  line  of  nodes  and  line  of  apsides  of  an  orbit ; 
also,  sometimes  the  obliquity  of  the  ecliptic. 


Conjunction. 
Quadrature. 
Opposition. 
Ascending  Node. 
Descending  Node. 


406 


INDEX 


[All  references,  unless  expressly  stated  to  the  contrary,  are  to  sections, 
not  to  pages.] 


Aberration,  of  light,  435;  determin- 
ing distance  of  sun,  436. 

Absolute  scale  of  star  magnitudes, 
346. 

Acceleration  of  rotation  at  the  sun's 
equator,  163. 

Achromatic  telescope,  406,  407. 

ADAMS,  J.  C.  (and  LEVEBRIER),  dis- 
covery of  Neptune,  283;  orbit  of 
the  Leonids,  327. 

Aerolite,  see  Meteorite. 

Age  of  the  sunand  planetary  system, 
193,  397-399. 

Albedo,  defined,  149,  235;  of  the 
moon  (Zollner),  149;  of  the  planets 
(Zollner),  242,  247,  253,  268,  276, 
281,  285. 

Algol,  or  Beta  Persei,  40,  351,  358, 
360. 

Alphabet,  the  Greek,  page  406. 

Altitude,  defined,  11 ;  parallels  of, 
11;  of  the  pole  equals  latitude, 
80. 

Andromeda,  constellation  of,  35; 
nebula  of,  377,  378;  temporary 
star  in  nebula,  355. 

Andromedes,  or  Bielids,  312,  326. 

Angular  measurements,  units  of,  8. 

Annual  or  heliocentric  parallax,  de- 
fined, 343 ;  methods  of  determin- 
ing it  for  the  stars  by  observation, 
441-444. 


Annular  eclipses,  201;    nebula    in 

Lyra,  377,  382. 
Anomalistic  year,  127. 
Anomalous  phenomena  in  comets, 

308. 

Apex  of  the  sun's  way,  342. 
Aphelion  defined,  120. 
Apogee  defined,  137. 
Apparent  motion  of  a  planet,  225- 

229 ;  motion  of  the  sun,  115-117 ; 

solar  time,  88.  A 

Apsides,  line  of,  defined,  120, 137  ^ 

the  moon's  orbit,  137. 
Aquarius,  78,  118. 
Aquila,  71. 
Arcs  of  meridian,  measurement  of, 

105,  110. 

Areas,  equal,  law  of,  121,  137,  220. 
Argo  Navis,  51. 

Ariel,  a  satellite  of  Uranus,  282. 
Aries,  first  of,  defined,  17 ;  constel- 
lation of,  38,  118. 

Asteroids,  or  minor  planets,  260-263. 
Astronomical    constants,   table  of, 

Table  I,  page  401 ;  day,  beginning 

of,  90;  symbols,  page  40(5;  unit, 

see  Distance  of  the  sun. 
Astronomy,  utility  of,  1. 
Atmosphere  of  the  moon,  148;  of 

Mars,  253;  of  Mercury,  242;  of 

Venus,  248. 
Attraction  of  gravitation,  its  law, 

221,  222. 


407 


408 


LESSONS  IN  ASTRONOMY 


Auriga,  41. 

Axis  of  the  earth,  13,  109 ;  motions 

of,  109. 
Azimuth  denned,  11. 


BARNARD,  E.  E.,  measures  of  diam- 
eters of  planets,  262, 267,  275,  285 ; 
seasonal  changes  on  Mars,  256; 
discovery  of  fifth  satellite  of  Ju- 
piter, 272;  of  comet  by  photog- 
raphy, 314* ;  photograph  of  Swift's 
comet,  314*. 

BAYER,  J.,  his  system  of  lettering 
the  stars,  24. 

Beginning  of  the  century,  130;  of 
the  day,  90,  98. 

BESSEL,  F.  W.,  dark  stars,  350,  360 ; 
first  measures  stellar  parallax, 
441,444. 

Bethlehem,  the  star  of,  355. 

BIELA'S  comet,  311,  312. 

Bielids,  or  Andromedes,  312, 324, 328. 

Binarystars,  368-371 ;  spectroscopic, 
373,  374. 

Bissextile  year,  129. 

BODE,  J.  E.,  his  law  of  planetary 
distances,  219. 

BOND,  W.  C.,  discovery  of  the 
"gauze  ring"  of  Saturn,  277; 
discovery  of  Hyperion,  280. 

Bootes,  59. 

BOYS,  C.  V.,  determination  of  the 
constant  of  gravitation  and  of  the 
density  of  the  earth,  113. 

BREDICHIN,  TH.,  his  theory  of 
comets'  tails,  307. 

Brightness,  of  comets,  291;  of  me- 
teors, 318 ;  of  stars,  and  causes  of 
difference,  345-350. 

BROOKS,  W.,  his  comets,  290,  299. 


C2ESAR,  JULIUS,  reformation  of  the 
calendar,  129. 


Calcium,  in  the  sun,  176 ;  in  f  aculae, 
165;  in  chromosphere  and  prom- 
inences, 181, 182*. 

Calendar,  the,  128-130. 

Calory,  the,  defined,  187. 

Camelopardalis,  31. 

CAMPBELL,  W.  W.,  spectrum  of 
Mars,  253 ;  radial  motion  of  stars, 
341 ;  spectra  of  nebulous  stars,  380. 

Canals  of  Mars,  256. 

Cancer,  52,  118. 

Canes  Venatici,  58. 

Canis  Major,  49. 

Canis  Minor,  48. 

Capricornus,  73,  118. 

Capture  theory  of  comets,  298. 

Cardinal  points  defined,  16. 

CARRINGTON,  R.,  discovery  of  the 
peculiar  law  of  the  sun's  rotation, 
163. 

CASSINI,  J.  D.,  discovers  division  in 
Saturn's  ring,  277. 

Cassiopeia,  28;  temporary  star  in, 
355. 

Catalogues  of  stars,  335. 

Celestial  globe,  described,  400,  401 ; 
sphere,  infinite,  6. 

Centaurus,  62. 

Centrifugal  force  due  to  earth's 
rotation,  111. 

Cepheus,  29. 

Ceres,  the  first  of  the  asteroids, 
260,  262. 

Cetus,  39. 

CHANDLER,  S.  C.,  variation  of  lati- 
tude, 109 ;  investigation  of  Brooks' 
comet,  1889-V,  299 ;  his  catalogue 
of  variable  stars,  361. 

Changes,  gradual,  in  the  brightness 
of  stars,  353;  on  the  surface  of 
the  moon,  155. 

CHARLOIS,  M.,  discoverer  of  aster- 
oids by  photography,  260. 

Chemical  constitution  of  the  sun, 
175, 176. 


INDEX 


409 


Chromosphere  of  the  sun,  180,  194 ; 
and  prominences  made  visible  by 
the  spectroscope,  182;  photog- 
raphy of,  182*. 

Chronograph,  the,  417. 

Chronometer,  the,  417;  longitude 
by,  96,  427. 

Circle,  meridian,  the,  81,  99,  418. 

Circles,  hour,  defined,  15. 

Circumpolar  stars,  latitude  by,  81. 

Civil  day  and  astronomical  day,  90. 

CLARK,  ALVAN,  AND  SONS,  makers 
of  great  telescopes,  412. 

CLARK,  A.  G.,  discovers  companion 
of  Sirius,  369. 

Classification  of  the  planets,  Hum- 
boldt,  217;  of  stellar  spectra, 
Secchi,  363;  of  variable  stars,  352. 

Clock,  the  astronomical,  417;  its 
rate  and  error,  92,  93,  417. 

Clusters  of  stars,  361,  376. 

Columba,  45. 

Colures  defined,  117. 

Coma  Berenices,  57. 

Comet,  Biela's,  311,  312;  Donati's, 
289;  Encke's,  293,  311;  Lexell- 
Brooks,  299;  Halley's,  293;  of 
1882,  313,  314. 

Comets,  anomalous  phenomena 
shown  by,  308;  attendant  com- 
panions, 314 ;  brightness  and  visi- 
bility, 291;  capture  theory  of 
their  origin,  298 ;  central  stripe  in 
tail,  308 ;  connection  with  meteors, 
327-329 ;  constitution  of,  300 ;  dan- 
ger from,  310;  density  of,  303; 
designation  and  nomenclature, 
290 ;  dimensions  of,  301 ;  elliptic, 
293,  297 ;  envelopes  in  head,  305 ; 
families  of,  297 ;  formation  of  the 
tail,  306;  their  light  and  spectra, 
304;  mass  of,  302;  nature  of, 
309;  number  of,  289;  orbits  of, 
292,  293;  periodic,  their  origin, 
297,  298;  photography  of,  314*; 


sheath  of  comet  of  1882,  313 ;  tails 
or  trains,  300,  306-308;  visitors  to 
the  solar  system,  296. 

Comet-groups,  294. 

Conic  sections,  the,  440. 

Conjunction,  defined,  132,  227. 

Constant,  solar,  defined  and  dis- 
cussed, 187;  of  the  equation  of 
light,  432 ;  of  aberration,  435. 

Constellations,  the,  4,  333.  (For  de- 
tailed description,  see  Chap.  II.) 

Constitution  of  comets,  300 ;  of  the 
sun,  194. 

Contraction  of  a  comet  nearing  the 
sun,  301;  of  the  sun,  Helmholtz's 
theory,  192,  396,  397. 

COPERNICUS,  rotation  of  the  earth, 
106 ;  his  system,  230. 

Corona  Borealis,  60. 

Corona,  the  solar,  183-185. 

Coronium,  hypothetical  element  of 
the  corona,  184. 

Correction  of  error  of  a  timepiece, 
92,  427. 

Corvus,  55. 

Cosmogony,  389-396. 

Crater,  55. 

Cygnus,  68. 


Dark  stars,  350,  360. 

DARWIN,  G.  H.,  motion  of  the  tides, 
211 ;  tidal  evolution,  393 ;  demon- 
strates that  a  meteoric  swarm 
behaves  like  a  gaseous  nebula, 
394. 

Day,  beginning  of,  98;  civil  and 
astronomical,  90. 

Declination,  defined,  14;  determina- 
tion of,  99,  100 ;  parallels  of,  14. 

Degrees  of  latitude,  length  of,  110. 

Deimos,  a  satellite  of  Mars,  258. 

DE  L'ISLE,  J.,  his  method  of  observ- 
ing a  transit  of  Venus,  437,  438. 

Delphinus,  74. 


410 


LESSONS  IN  ASTRONOMY 


Density,  of  comets,  303;  of  the 
earth,  113;  of  the  moon,  143;  of 
the  sun,  161. 

Designation  and  nomenclature  of 
comets,  290 ;  of  the  stars,  24,  334 ; 
of  variable  stars,  361. 

DESLANDRES,  H.,  photography  of 
solar  prominences,  182*. 

Diameter  of  a  planet,  how  deter- 
mined, 232. 

Difference  of  brightness  in  stars,  its 
causes,  350. 

Diffraction,  telescopic,  408. 

Diffraction  grating,  the,  171,  note. 

Dione,  a  satellite  of  Saturn,  280. 

Disk,  spurious,  of  a  star,  408. 

Displacement  of  spectrum  lines  by 
motion  in  line  of  sight,  179,  341, 
373. 

Distance,  of  a  body  as  depending  on 
its  parallax,  140;  of  the  moon, 
141;  of  the  nebulae,  382;  of  the 
planets  from  the  sun,  Table  II, 
page  402;  of  the  stars,  343,  441- 
444;  of  the  sun,  by  the  equation 
of  light,  434 ;  of  the  sun,  by  aber- 
ration of  light,  436;  of  the  sun, 
by  its  parallax,  437. 

Distribution  of  the  nebulas,  382 ;  of 
the  stars  in  the  heavens,  384 ;  of 
sun-spots,  169. 

Diurnal  or  geocentric  parallax  de- 
nned, 139 ;  rotation  of  the  heavens, 
12. 

DOPPLER,  C.,  his  principle,  179, 
341,  373. 

Double  stars,  366,  367 ;  optical  and 
physical,  distinguished,  367. 

Draco,  30. 

DRAPER,  H.,  photograph  of  the 
nebula  of  Orion,  378 ;  photographs 
of  star  spectra,  364. 

Duration  of  solar  eclipses,  203 ;  prob- 
able, of  the  solar  system,  193, 
397-399. 


E 

Earth,  the,  astronomical  facts  re- 
lating to  it,  102 ;  its  density,  113 ; 
dimensions  of,  105,  110,  Table  I. 
page  401 ;  ellipticity  or  oblateness 
determined,  110;  its  interior  con- 
stitution, 114;  mass,  113;  orbital 
motion  of,  115-122,  428;  its  orbit, 
changes  in,  122;  its  rotation,  in- 
variability of,  108;  its  rotation, 
proofs  of,  107;  shadow  of,  its 
dimensions,  196 ;  surface  area  and 
volume,  112 ;  velocity  in  its  orbit, 
158. 

Earth-shine  on  the  moon*  147. 

Ebb  defined,  210. 

Eccentricity  of  the  earth's  orbit, 
119;  of  an  ellipse,  defined,  119, 
429. 

Eclipses,  frequency  of,  206 ;  of  Jupi- 
ter's satellites,  273;  lunar,  197- 
199;  Oppolzer's  canon  of,  205; 
number  in  a  year,  206;  recur- 
rence of,  207 ;  solar,  duration  of, 
203;  solar,  phenomena  of,  204; 
solar,  varieties  of,  —  total,  annu- 
lar, and  partial,  201,  202. 

Ecliptic,  the,  defined,  116 ;  obliquity 
of,  116 ;  poles  of,  117. 

Elements,  chemical,  recognized  in 
the  stars,  362;  chemical,  recog- 
nized in  the  sun,  176;  of  the 
planets'  orbits,  Table  II,  page 
402. 

Ellipse,  the,  defined  and  described, 
429,  439,  440. 

Elliptic  comets,  292,  293. 

Ellipticity,  or  oblateness  of  the 
earth,  110. 

Elongation  defined,  132,  227-. 

Enceladus,  a  satellite  of  Saturn, 
280. 

ENCKE,  J.  F.,  his  comet,  293,  311. 

Energy  of  the  solar  radiation,  188, 
189. 


INDEX 


411 


Envelopes  in  the  head  of  a  comet, 

305,  314. 
Equation  of  light,  431-433 ;  of  time, 

89. 
Equator,  celestial    or    equinoctial, 

denned,  14. 
Equatorial  acceleration  of  the  sun's 

surface  rotation,  163. 
Equatorial  telescope,  the,  414;  its 

use  in  determining  the  place  of  a 

heavenly  hody,  100. 
Equinoctial,  the,  or  celestial  equa- 
tor, defined,  14. 

Equinox,  vernal,  defined,  17,  11G. 
Equinoxes,  precession  of,  125,  126. 
Equuleus,  75. 
Eridanus,  44. 
Eros,  asteroid,  261,  262*. 
Error  or  correction  of  a  timepiece, 

92,  93,  417. 
Eruptive  prominences  on  the  sun, 

182. 

Establishment  of  a  port,  210. 
Eyepieces,  telescopic,  various  forms 

of,  409. 


Faculae,  solar,  165. 

Families  of  comets,  297. 

FAYE,  H.,  depth  of  sun-spots,  168; 
modification  of  the  nebular  hy- 
pothesis, 393. 

Filar  micrometer,  the,  415. 

FIZEAU,  H.  L.,  the  Doppler-Fizeau 
principle,  179 ;  measure  of  velocity 
of  light,  434. 

Flood  tide,  210. 

Force,  repulsive,  of  light,  306. 

Form  of  the  earth's  orbit  deter- 
mined, 428. 

FOUCAUI/T,  L.,  his  pendulum  experi- 
ment, 107. 

FRAUNHOFER,  J.,  lines  in  the  solar 
spectrum,  175,  note. 

Frequency  of  eclipses,  206. 


Galaxy,  the,  383. 

GALILEO,  G.,  his  discovery  of  Ju- 
piter's satellites,  272 ;  discovery  of 
phases  of  Venus,  247 ;  discovery 
of  Saturn's  ring,  277 ;  discovery  of 
sun-spots,  169 ;  his  telescope,  402. 

GALLE,  J.  G.,  the  first  to  see  Nep- 
tune, 283,  note. 

Gemination  of  the  canals  of  Mars, 
256. 

Gemini,  47,  118. 

Genesis  of  the  planetary  system, 
390,  391. 

Geocentric  parallax,  139. 

Gibbous  phase  defined,  146. 

Globe,  the  celestial,  described,  400, 
401. 

Grating,  diffraction,  171,  note. 

Gravitation,  221,  222. 

Gravity,  at  the  moon's  surface,  143 ; 
at  the  pole  and  equator  of  the 
earth,  111;  at  the  sun's  surface, 
161 ;  superficial,  of  a  planet,  how 
determined,  233. 

Greek  alphabet,  the,  page  406. 

Gregorian  calendar,  the,  130. 

Groups,  cometary,  294. 

Grus,  79. 

Gyroscope  illustrating  the  cause  of 
the  seasons,  123. 


H  and  K  lines  of  calcium,  165,  176, 

181,182*. 

Habitability  of  Mars,  259. 
HALE,  G.  E.,  photographs  of  the 

moon,  156  * ;  of  solar  prominences, 

182*. 
HALL,  A.,  discovery  of  the  satellites 

of  Mars,  258;  mass  of  Saturn's 

rings,  277. 
HALLE Y,  E.,  discovers  the  proper 

motion  of  stars,  339 ;  his  periodic 

comet,  293,  314 


412 


LESSONS  IN  ASTRONOMY 


HARDING,  C.,  discovers  Juno,  260. 

Harmonic  law,  Kepler's,  220,  430. 

Harvest  and  hunter's  moons,  the, 
136. 

Heat,  of  meteors,  its  explanation, 
318;  from  the  moon,  150;  from 
the  stars,  348,  note;  of  the  sun, 
its  constancy,  191 ;  of  the  sun,  its 
intensity,  190;  of  the  sun,  its 
maintenance,  192;  of  the  sun,  its 
quantity,  187, 189. 

Heavenly  hodies,  defined  and  enu- 
merated, 2;  apparent  place  of,  7. 

Heliocentric  or  annual  parallax, 
defined,  139,  343. 

Helium,  hypothetical  element  in 
the  sun,  181 ;  its  identification 
as  a  terrestrial  element  in  uran- 
inite,  181 ;  in  temporary  and  vari- 
able stars,  355,  356;  in  nebulae, 
380. 

HELMHOLTZ,  H.  VON,  his  theory  of 
the  sun's  heat,  192. 

HENCKE,  L.,  discovers  Astraea,  260. 

Hercules,  66. 

HERSCHEL,  SIR  J.,  illustration  of 
the  solar  system,  238 ;  his  names 
for  the  satellites  of  Saturn  and 
Uranus,  280,  282. 

HERSCHEL,  SIR  W.,  discovery  of 
Uranus,  281 ;  his  great  telescope, 
412 ;  relation  between  nebulae  and 
stars,  395. 

HERSCHELS,  the,  their  star-gauges, 
384. 

HIPPARCHUS,  120,  125,  335,  345. 

Horizon,  defined,  rational  and  visi- 
ble, 10. 

Horizontal  parallax,  139. 

Hour-angle  defined,  422. 

Hour-circles  defined,  15. 

Hourly  number  of  meteors,  321. 

HUGGINS,  SIR  WILLIAM,  observes 
spectrum  of  Mars,  253;  observes 
spectrum  of  Mercury,  242;  ob- 


serves spectrum  of  nebulas,  380; 
observes  spectrum  of  stars,  362; 
observes  spectrum  of  temporary 
star  of  1866,  355;  spectroscopic 
measures  of  star  motions,  341. 

HUMBOLDT,  A.  VON,  his  classifica- 
tion  of  the  planets,  217. 

Hunter's  moon,  the,  136. 

HUYGHENS,  CHR.,  his  discovery  of 
Saturn's  ring,  277;  discovery  of 
Titan,  280;  invention  of  the  pen- 
dulum clock,  417. 

Hydra,  55. 

Hyperbola,  the,  439,  440. 

Hyperion,  a  satellite  of  Saturn,  280. 


lapetus,  the  remotest  satellite  of 

Saturn, 280. 
Identification  of  helium,  181 ;  of  the 

orbits    of    certain    comets    and 

meteors,  328. 
Illuminating  power  of  a  telescope, 

405. 
Illumination  of    the    moon's    disk 

during  a  lunar  eclipse,  198. 
Illustration  of  the  proportions   of 

the  solar  system,  238. 
Influence  of  the  moon  on  the  earth, 

151;   of  sun-spots  on  the  earth, 

170. 
Intensity  of  the  sun's  heat,  189-190 ; 

of  the  sun's  light,  186. 
Intramercurian  planets,  264. 
Invariability  of  the  earth's  rotation. 

108 ;  of  the  length  of  the  year  and 

distance  from  the  sun,  122. 
Iron  in  comets,  314 ;  in  meteorites, 

316 ;  in  stars,  362 ;  in  the  sun,  175. 


Julian  calendar,  the,  129. 
Juno,  the  third  asteroid,  260,  262. 
Jupiter  (the  planet),   266-271;   his 
belts,   red   spot,   and    other 


INDEX 


413 


markings,  268,  271 ;  his  rotation, 
270;    his    satellites,    and    their 
eclipses,  272,  273. 
Jupiter's  family  of  comets,  297. 


KANT,  I.,  a  proposer  of  the  nebular 
hypothesis,  391. 

KEELEB,  J.  E.,  spectroscopic  obser- 
vation of  the  rings  of  Saturn,  279; 
radial  motion  of  stars,  341 ;  types 
of  stellar  spectra,  363;  photo- 
graphs of  nebulae,  378;  spectra 
and  motions  of  nebulae,  380. 

KELVIN,  LORD,  formerly  Sir  Wil- 
liam Thomson,  114,  318,  396. 

KEPLER,  J.,  his  laws  of  planetary 
motion,  121,  220,  430. 

KIRCHHOFF,  G.  R.,  fundamental 
principles  of  spectrum  analysis, 
173. 

L 

Lacerta,  76. 

LAGRANGE,  J.  L.,  stability  of  the 
solar  system,  288*. 

LANGLEY,  S.  P.,  his  value  of  the 
solar  constant,  187. 

LAPLACE,  P.  S.,  his  capture  theory 
of  comets,  298;  his  nebular  hy- 
pothesis, 392,  393;  stability  of 
the  solar  system,  288*. 

LASSELL,  W.,  his  discovery  of  Ariel 
and  Umbriel,  282;  his  discovery 
of  the  satellite  of  Neptune,  286. 

Latitude  (celestial)  defined,  20; 
(terrestrial)  defined,  80 ;  length  of 
degrees,  110;  methods  of  deter- 
mining, 81,  424,  426;  variations 
of,  109. 

Law,  Bode's,  219 ;  of  the  earth's  or- 
bital motion,  121 ;  of  gravitation, 
221,  222. 

Laws,  Kepler's,  121,  220,  430. 

Leap  year,  129,  130. 

Leo,  53,  118. 


Leo  Minor,  54. 

Leonids,  the,  324,  325,  326,  329. 

Lepus,  45. 

LEVERRIER,  J.  U.  (and  ADAMS), 
discovery  of  Neptune,  283 ;  on  the 
origin  of  the  Leonids,  329. 

Libra,  61,  118. 

Librations  of  the  moon,  145. 

Lick  observatory,  telescope,  412; 
various  observations,  156*,  253, 
256,  262,  267,  272,  275,  279,  314*, 
341,  380. 

Light,  aberration  of,  435,  436;  of 
comets,  291 ;  equation  of,  the, 
431,  432;  of  the  moon,  149 ;  of  the 
sun,  its  intensity,  186;  repulsive 
force  of,  306;  of  the  stars,  348- 
350;  velocity  of,  used  to  deter- 
mine the  distance  of  the  sun, 
434,  436 ;  the  zodiacal,  265. 

Light-ratio  of  the  scale  of  stellar 
magnitude,  346. 

Light-year,  the,  344. 

Local  time,  97 ;  time  from  altitude 
of  the  sun,  427 ;  time  by  transit- 
instrument,  93,  416. 

LOCKYER,  SIR  J.  N.,  his  meteoritic 
hypothesis,  330,  394;  on  spectra 
of  nebulae,  380. 

Longitude  and  latitude  (celestial), 
20;  (terrestrial),  defined, 94;  (ter- 
restrial), methods  of  determining, 
95,  96,  427. 

LOWELL,  P.,  observations  on  Mer- 
cury,  243;  on  Venus,  249;  on 
Mars,  256. 

Lunar,  see  Moon. 

Lupus,  62. 

Lynx,  46. 

Lyra,  67. 

Magnesium,  in  the  sun,  176;  in  the 

stars,  362. 
Magnifying  power  of  a  telescope, 

404. 


414 


LESSONS  IN  ASTRONOMY 


Magnitudes,  star,  345-347 ;  star,  ab- 
solute scale  of,  346;  star,  and 
telescopic  power,  347. 

Mars  (the  planet),  251-257;  habita- 
bility  of,  259;  map  of  the  planet, 
257 ;  satellites,  258 ;  Schiaparelli's 
observations,  etc.,  256;  telescopic 
aspect,  rotation,  etc.,  253,254. 

Mass,  definition,  113;  of  comets, 
302 ;  of  earth,  113 ;  of  moon,  143 ; 
of  a  planet,  how  determined,  233 ; 
of  shooting-stars,  how  estimated, 
323;  of  the  sun,  161. 

Masses  of  binary  stars,  371. 

Mazapil,  meteorite  of,  326. 

Mean  and  apparent  places  of  stars, 
336 ;  and  apparent  solar  time,  88- 
89. 

Mercury  (the  planet),  239-244 ;  rota- 
tion of,  243 ;  transits  of,  244. 

Meridian  (celestial),  defined,  11,  15, 
16;  (terrestrial),  arcs  of,  meas- 
ured, 105, 110;  circle,  the,  81,  99, 
418. 

Meteoritic  hypothesis  (Lockyer) , 
330,  394 ;  showers,  324-326. 

Meteorite  of  Mazapil,  326. 

Meteorites,  315 ;  their  constituents, 
316 ;  their  fall,  315. 

Meteors,  ashes  of,  323;  connection 
with  comets,  327-329;  heat  and 
light,  318;  observation  of,  317; 
origin  of,  319 ;  path  and  velocity, 
317. 

MICHELSON,  A.  A.,  the  velocity  of 
light,  436. 

Micrometer,  the,  415. 

Midnight  sun,  the,  86. 

Milky  Way,  the,  383. 

Mimas,  the  inner  satellite  of  Saturn, 
280. 

Mira  Ceti,  356. 

Missing  and  new  stars,  353. 

Monoceros,  50. 

Month,  sidereal  and  synodic,  133. 


Moon,  its  albedo,  149;  its  atmos- 
phere discussed,  148;  changes  on 
its  surface,  155 ;  character  of  its 
surface,  153 ;  density,  143 ;  diam- 
eter, surface  area,  and  bulk, 
142 ;  distance  and  parallax,  141 ; 
eclipses  of,  195-199;  heat,  150;  in- 
fluence on  the  earth,  151 ;  libra- 
tions,  145 ;  light  and  albedo,  149 ; 
maps,  154,  156;  mass,  density, 
and  gravity,  143;  motion  (in  gen- 
eral), 132-135;  nomenclature  of 
objects  on  surface,  156;  perturba- 
tions of,  134 ;  phases,  146 ;  photog- 
raphy of,  156*;  rotation,  144; 
shadow  of,  200 ;  surface  structure, 
153;  telescopic  appearance,  152; 
temperature,  150 ;  water  not  pres- 
ent, 148. 

Motion,  apparent  diurnal,  of  the 
heavens,  12,  13;  of  the  moon, 
132-134;  of  a  planet,  225,  226, 
229;  of  the  sun,  115-117;  in  line 
of  sight,  or  radial  motion,  effect 
on  spectrum,  179,  341,  373,  574; 
of  the  sun  in  space,  342. 

Motions  of  stars,  338-341.., 

Mountains,  lunar,  153.  156. 

Mounting  of  a  telescope,  414. 

Multiple  stars,  375. 

N 

Nadir  defined,  10. 

Nadir  point  of  meridian  circle,  419. 

Names  of  planets,  218 ;  of  satellites 
of  the  planets,  258,  280,  282,  also 
Table  III,  page  403. 

Neap  tide,  210. 

Nebulae,  the,  377-382;  changes  in, 
379;  distance  and  distribution, 
382;  drawings  and  photographs 
of,  378;  spectra  of,  380,  381. 

Nebular  hypothesis,  the,  392,  393. 

Negative  eyepieces,  409. 

Neptune  (the  planet),  283-287. 


INDEX 


415 


NEWCOMB,  S.,  on  the  age  and  dura- 
tion of  the  system,  193;  and 
MICHELSON,  the  velocity  of  light, 
436. 

NEWTON,  H.  A.,  estimate  of  the  daily     | 
number  of  meteors,  321;  investi- 
gation of  the  orbit  of  the  Leonids, 
327 ;  nature  of  comets,  309. 

NEWTON,  SIR  ISAAC,  law  of  gravi- 
tation, 221,  222. 

Nodes  of  the  moon's  orbit  and  their 
regression,  134;  of  the  planetary 
orbits,  224. 

NORDENSKIOLD,  A.  E.  VON,  ashes 
of  meteors,  323. 

Norma,  64. 

Novse,  or  temporary  stars,  355, 355*. 

Number,  of  comets,  289 ;  of  eclipses 
in  a  saros,  207;  of  eclipses  in  a 
year,  206 ;  of  the  stars,  332. 


Oases,  on  Mars,  256. 

Oberon,  a  satellite  of  Uranus,  282. 

Oblateness    or    ellipticity    of    the 

earth,  defined,  110. 
Oblique  sphere,  85. 
Obliquity  of  the  ecliptic^  116. 
OLBERS,  H.  W.  M.,  DR.,  discovers 

Pallas  and  Vesta,  260. 
Ophiuchus,  65. 
OPPOLZER,  TH.  VON,  his  canon  of 

eclipses,  205. 

Opposition  denned,  132,  227 v 
Orbit,  of  the  earth,  its  form,  etc., 

115,  122,  428;  of  the  moon,  137; 

parallactic,  of  a  star,  442. 
Orbital  motion  of  the  earth,  proof 

of,  115. 
Orbits,    of    binary    stars,    370;    of 

comets,  292 ;  of  planets,  223. 
Origin  of  the    asteroids,    263;    of 

meteors,  319 ;  of  periodic  comets, 

297. 
Orion,  43;  nebula  of,  378. 


PALISA,  J.,  discovery  of  asteroids, 
260. 

Pallas,  the  second  asteroid,  260. 

Parabola,  the,  439,  440. 

Parallax,  annual  or  heliocentric,  of 
the  stars,  139,  343,  441-444 ;  diur- 
nal or  geocentric,  139 ;  solar,  by 
transit  of  Venus,  de  1'Isle's 
method,  437;  of  a  nebula,  382; 
of  stars,  343;  stellar,  how  deter- 
mined, 441-444. 

Parallaxes,  stellar,  table  of,  Table 
V,  page  405. 

Parallel  sphere,  84. 

Pegasus,  77. 

Pendulum  used  to  determine  earth's 
form,  111;  Foucault,  107. 

Perigee  defined,  137. 

Perihelion  defined,  120. 

Periodicity  of  sun-spots,  169. 

Periods  of  the  planets,  218 ;  sidereal 
and  synodic,  133,  162,  228. 

Persei,  Nova  (1901),  355*. 

Perseids,  the,  324-326,  328,  329. 

Perseus,  40. 

Perturbations,  lunar,  134;  plane- 
tary, 122,  288*. 

PETERS,  C.  H.  F.,  asteroid  dis- 
coveries, 260. 

Phase  of  Mars,  253. 

Phases,  of  Mercury  and  Venus,  242, 
247 ;  of  the  moon,  146 ;  of  Saturn's 
rings,  278. 

Phobos,  a  satellite  of  Mars,  258. 

Phoabe,  name  assigned  to  the  ninth 
satellite  of  Saturn,  280. 

Phoenix,  39. 

Photographic  power  of  eclipsed 
moon,  198;  star  charts,  337;  tele- 
scopes, 337. 

Photographs,  of  solar  prominences, 
182* ;  applied  to  discovery  of  aster- 
oids, 260 ;  of  comets,  314* ;  of  neb- 
ulae, 378 ;  of  star  spectra,  341, 364. 


416 


LESSONS  IN  ASTRONOMY 


Photography,  solar,  164. 

Photometry,  stellar,  348,  349. 

Photosphere,  the,  165,  194. 

PIAZZI,  G.,  discovers  Ceres,  260. 

PICKERING,  E.  C.,  determination 
of  rotation  period  of  Eros  by 
photometric  observations,  262*; 
photographs  of  star  spectra,  364, 
373;  photometric  observations  of 
eclipses  of  Jupiter's  satellites, 
433;  photometric  measures  of 
stellar  magnitudes,  346. 

PICKERING,  W.  H.,  observations  on 
moon,  155 ;  on  Jupiter's  satellites, 
272;  announces  a  ninth  satellite 
of  Saturn,'  280. 

Pisces,  36,  118. 

Piscis  Australis,  79. 

Place,  of  .a  heavenly  body,  defined, 
7 ;  of  a  heavenly  body,  how  deter- 
mined by  observation,  99,  100 ;  of 
a  ship,  how  determined,  426,  427. 

Planet,  albedo  of,  defined,  231,  235 ; 
apparent  motion  of,  225-229;  di- 
ameter and  volume,  how  meas- 
ured, 232 ;  mass  and  density,  how 
determined,  233 ;  rotation  on  axis 
determined,  234,  262*;  satellite 
system,  how  investigated,'  236; 
superficial  gravity  determined, 
233. 

Planetary  data,  their  relative  accu- 
racy, 237  ;  system,  its  genesis,  age, 
and  duration,  390-398 ;  its  stabil- 
ity, 288*. 

Planetesimal  hypothesis,  page  358. 

Planets,  Humboldt's  classification, 
217;  list  of,  218;  intramercurian, 
264;  minor,  260-263;  possibly 
attending  stars,  372;  table  of 
elements,  Table  II,  page  402; 
table  of  names,  symbols,  etc., 
218. 

Pleiades,  the,  42,  376. 

Pointers,  the,  12,  26. 


Pole  (celestial),  altitude  of,  equals 
latitude,  80 ;  defined,  13 ;  effect  of 
precession,  126 ;  (terrestrial),  diur- 
nal phenomena  near  it,  83 ;  mo- 
tion of,  109. 

Pole-star,  former,  Alpha  Draconis, 
126 ;  how  recognized,  12. 

Positive  eyepieces,  409. 

Precession  of  the  equinoxes,  125, 
126. 

Pressure,  its  effect  on  wave-length 
of  light,  179. 

Prime  vertical,  the,  11. 

PROCTOR,  R.  A.,  sun-spots,  168. 

Prominences,  the  solar,  181,  182, 
194. 

Proper  motion  of  stars,  339. 

Ptolemaic  system,  the,  230. 

PTOLEMY,  CLAUDIUS,  4,  230. 


Quadrature  defined,  132,  227. 
Quiescent  prominences,  182. 

R 

Radial  motion,  or  motion  in  line  of 
sight,  measured  by  Poppler's 
principle,  179,  341,  373,  374. 

Radiant,  the,  of  a  meteoric  shower, 
324. 

Radius  vector  defined,  120. 

RAMSAY,  W.,  identification  of  he- 
lium, 181. 

Rate  of  a  timepiece  defined,  417. 

Rectification  of  a  globe,  401. 

Recurrence  of  eclipses,  207. 

Red  spot  of  Jupiter,  271. 

Reflecting  telescope,  the,  411,  413. 

Refracting  telescope,  the,  403-407, 
413. 

Refraction,  astronomical,  82. 

Repulsive  force  of  light,  306. 

Reticle,  the,  410,  416. 

Retrograde  and  retrogression  de- 
fined, 226. 


INDEX 


417 


Reversing  layer,  177. 

Rhea,  a  satellite  of  Saturn,  280. 

Right  ascension,  defined,  18, 93 ;  how 
determined  by  observation,  99, 
100. 

Right  sphere,  the,  83. 

Rings  of  Saturn,  the,  277-279. 

ROBERTS,  I.,  photographs  of  neb- 
ulje,  378. 

ROSSE,  LORD,  heat  of  the  moon,  150 ; 
his  great  reflector,  412. 

Rotation,  apparent  diurnal,  of  the 
heavens,  12 ;  definition  of ,  144;  dis- 
tinguished from  revolution,  106, 
note ;  of  earth,  its  effect  on  grav- 
ity, 111 ;  of  earth,  proofs  of,  107 ; 
of  earth,  variability  of,  108;  of 
the  moon,  144 ;  of  the  sun,  162, 163. 

Rotation  period,  of  Eros,  262*;  of 
Jupiter,  270 ;  of  Mars,  254 ;  of  Mer- 
cury, 243 ;  of  a  planet,  how  ascer- 
tained, 234,  262*;  of  Saturn,  275; 
of  Venus,  249. 


Sagitta,  70. 

Sagittarius,  72,  118. 

Saros,  the,  207. 

Satellite  system,  how  investigated, 

236 ;  systems,  table  of,  Table  III, 

page  403. 
Satellites,  of  Jupiter,  272 ;  of  Mars, 

258 ;  of  Neptune,  286 ;  of  Saturn, 

280;  of  Uranus,  282. 
Saturn  (the  planet),  274-280. 
Scale  of  stellar  magnitudes,  346. 
SCHIAPARELLI,  G.  V.,  identification 

of  cometary  and  meteoric  orbits, 

328;   observations  of  Mars,  256; 

rotation  of  Mercury  and  Venus, 

243,  249. 
SCHMIDT,  J.,  his  map  of  the  moon, 

156. 

SCHWABE,  S.  H.,  discovers  perio- 
dicity of  sun-spots,  169. 


Scintillation  of  the  stars,  365. 

Scorpio,  63,  118. 

Sea,  position  of  ship  at,  how  found, 

426,  427. 

Seasons,  explanation  of,  123-124. 
SECCHI,  A.,  on  stellar  spectra,  363; 

on  sun-spots,  168. 
Secondary  spectrum  of  achromatic 

object-glass,  407. 
SEE,  T.  J.  J.,  measures  of  planets' 

diameters,  267,  281 ;  evolution  of 

binary  systems,  370. 
Serpens,  65. 
Serpentarius,  65. 
Sextant,  the,  420,  421. 
Shadow,  of  the  earth,  its  dimensions, 

196 ;  of  the  moon,  its  dimensions, 

200 ;  of  the  moon,  its  velocity,  203. 
Ship  at  sea,   determination  of  its 

position,  426,  427. 
Shooting-stars  (see  also   Meteors), 

320-324 ;  ashes  of,  323 ;  brightness 

of,  323;  elevation  and  path,  322; 

mass  of,  323;  materials  of,  323; 

nature    of,    320;    number,  daily 

and    hourly,  321;    radiant,   324; 

showers  of,  324-326 ;  spectrum  o2, 

323 ;  velocity  of,  322. 
Showers,  meteoric,  324-326. 
Sidereal,  and  synodic  months,  133  ; 

and  synodic  periods  of  planets, 

228 ;  time  defined,  91 ;  year,  127. 
Signs  of  the  zodiac,  118;  effect  of 

precession  on  them,  126. 
Sirius,   its    companion,  369;    light 

compared  with  that  of  the  sun, 

349 ;  its  mass  compared  with  that 

of  the  sun,  370. 
Solar,  constant,  the,  187 ;  parallax, 

158;  time,  mean  and   apparent, 

88,  89. 

Solstice  defined,  117. 
SOSIGENES  and  the  calendar,  129. 
Spectroscope,  its  principle  and  con- 
struction,  171,  172;  slitless,  364, 


418 


LESSONS  IN  ASTRONOMY 


445;  used  to  observe  the  solar 
prominences,  182;  used  to  meas- 
ure motions  in  line  of  sight,  178, 
179,  341,  373,  374. 

Spectroscopic  binaries,  360, 373, 374. 

Spectrum,  of  the  chromosphere  and 
prominences,  181;  of  comets  in 
general,  304;  of  the  comet  of 
1882,  314;  of  meteors,  323;  of 
nebulae,  380,  381;  of  a  shooting- 
star,  323;  of  stars,  362-364;  the 
solar,  172-175 ;  of  the  solar  corona, 
184;  of  a  sun-spot,  178. 

Spectrum  analysis,  fundamental 
principles,  173. 

Speculum  of  a  reflecting  telescope, 
411. 

Sphere,  celestial,  the,  6 ;  doctrine  of 
the,  9-20. 

SPOERER,  G.,  peculiar  law  of  sun- 
spot  latitude,  169. 

Spots,  solar,  see  Sun-spots. 

Spring  tide  denned,  210. 

Stability  of  the  planetary  system, 
288*. 

Standard  time,  97. 

Stars,  binary,  368-371,  373,  374; 
catalogues  of,  335;  charts  of, 
337;  clusters  of,  361,  376;  dark, 

350,  360 ;  designation  and  nomen- 
clature, 24,  334;    dimensions  of, 

351,  360;   distance  of,  343,  344; 
distribution  of,  384 ;  double,  366, 
367;    gravitation    among    them, 
368,  371,  386;  heat  from  them, 
348,  note;  light  of  certain  stars 
compared  with  sunlight,  348,  349 ; 
magnitudes  and  brightness,  345- 
350 ;  mean  and  apparent  places  of, 
336 ;  missing  and  new,  353 ;  mo- 
tions of,  338-342;  multiple,  375; 
new,  353,  355,  355*;  number  of, 
332;    parallax  of,   343,    441-444, 
Table  V,  page  405 ;  shooting  (see 
Shooting-stars,    also     Meteors) ; 


spectra  of,  362-364;  system  of 
the,  386;  temporary,  355,  355*; 
total  amount  of  light  from  the, 
348 ;  twinkling  of,  365 ;  variable, 
352-361,  Table  IV,  page  404. 

Star-gauges  of  the  Herschels,  384. 

Starlight,  its  total  amount,  348. 

Stellar  parallaxes,  table  of,  Table 
V,  page  405;  photometry,  348, 
349. 

Structure  of  the  stellar  universe, 
385. 

STRUVE,  H.,  mass,  of  Saturn's 
ring,  277;  measures  of  Neptune, 
285. 

Sun,  age  and  duration  of,  193, 
397,  398 ;  apparent  motion  in  the 
heavens,  115-117;  its  chromo- 
sphere, 180 ;  its  constitution,  194 ; 
its  corona,  183-185;  its  density, 
161 ;  dimensions  of,  160 ;  distance 
of,  158,  159,  434-438;  elements 
recognized  in  it,  176 ;  faculae,  165 ; 
gravity  on  its  surface,  161 ;  heat 
of,  quantity,  intensity,  and  main- 
tenance, 187-192;  light  of,  its 
intensity,  186 ;  mass  of,  161 ;  mo- 
tion in  space,  342;  parallax  of, 
159,  434-^38;  prominences,  181, 
182,  194;  reversing  layer,  the, 
177,  194;  rotation  of,  162,  163; 
spectrum  of,  172,  175;  tempera- 
ture of,  190;  temperature  dimin- 
ishing, Lockyer,  396,  note. 

Sun-spots,  appearance  and  nature, 
166, 167 ;  cause  of,  168 ;  distribu- 
tion of,  169;  Spoerer's  law  of 
latitude,  169;  influence  on  the 
earth,  170;  periodicity  of,  169; 
spectrum  of,  178. 

Superficial  gravity  of  a  planet,  how 
determined,  233. 

Surface  structure  of  the  moon,  153, 
154. 

Swarms,  meteoric,  324-329. 


INDEX 


419 


Synodic  and  sidereal  months,  133; 
and  sidereal  periods  of  planets, 
228. 

System,  planetary,  its  age  and  dura- 
tion, 397-399;  its  genesis  and 
evolution,  390-393;  its  stability, 
288* ;  stellar,  its  probable  nature, 
386-388. 

Syzygy  denned,  132. 


Tables :  astronomical  constants, 
Table  I,  page  401;  astronomical 
symbols,  page  406 ;  'binary  stars, 
orbits  and  masses,  370;  Bode's 
law,  219;  constellations,  show- 
ing place  in  heavens,  page  63; 
Greek  alphabet,  page  406 ;  moon, 
names  of  principal  objects,  156; 
planet's  elements,  Table  II,  page 
402;  planets'  names,  distances, 
etc.,  approximate,  218;  satellite 
systems,  Table  III,  page  403; 
stellar  parallaxes  and  proper  mo- 
tions, Table  V,  page  405 ;  variable 
stars,  Table  IV,  page  404. 

Tails  of  comets,  300,  301,  SOS- 
SOS. 

Taurus,  42. 

Telegraph,  longitude  by,  95. 

Telescope,  achromatic,  406,  407; 
eyepieces  of,  409;  general  prin- 
ciples of,  402 ;  illuminating  power, 
405 ;  magnifying  power,  404 ;  mag- 
nitude of  stars  visible  with  a 
given  aperture,  347 ;  mounting  of, 
414;  reflecting,  411;  simple  re- 
fracting, 403. 

Telescopes,  great,  412. 

TEMPEL,  E.  W.,  his  comet,  329,  330. 

Temperature  of  the  moon,  150;  of 
the  sun,  190. 

Temporary  stars,  355,  355*. 

Terminator,  the,  defined  and  de- 
scribed, 146. 


Tethys,  a  satellite  of  Saturn,  280. 

THOMSON,  SIB  W.  (now  LORD 
KELVIN),  internal  heat  of  the 
earth,  396 ;  heat  of  meteors,  318 ; 
rigidity  of  the  earth,  114. 

Tidal  wave,  course  of,  213. 

Tides;  definitions  relating  to,  210; 
due  mainly  to  moon's  action,  209; 
explanation  of,  208,  209,  211,  212; 
height  of,  214;  in  rivers,  215; 
motion  of,  211^213. 

Time,  equation  of,  89;  local,  from 
sun's  altitude,  427;  methods  of 
determining,  92,  93,  427 ;  relation 
to  hour-angle,  422;  sidereal,  de- 
fined, 91;  solar  —  mean  and  ap- 
parent, 88,  89;  standard,  defined, 
97. 

Titan,  satellite  of  Saturn,  280. 

Titania,  satellite  of  Uranus,  282^ 

Total  and  annular  eclipses,  197, 198, 
201. 

Trains  of  meteors,  315. 

Transit  or  meridian  circle,  81,  99, 
418. 

Transit-instrument,  the,  92,  416. 

Transits,  of  Mercury,  244 ;  of  Venus, 
250. 

Triangulum,  37. 

Tropical  year,  the,  127. 

Twinkling  of  the  stars,  365. 

TYCHO  BRAKE,  his  temporary  star 
in  Cassiopeia,  355. 


Ultra-Neptunian  planet,  288. 
Umbriel,    a    satellite    of    Uranus, 

282. 

Universe,  stellar,  its  structure,  385. 
Uranography  defined,  5. 
Uranolite,  see  Meteorite. 
Uranus  (the  planet),  281,  282. 
Ursa  Major,  26. 
Ursa  Minor,  27. 
Utility  of  astronomy,  1. 


420 


LESSONS  IN  ASTKONOMY 


Vanishing  point,  6,  note. 

Variable  stars,  352-361;  in  star 
clusters,  361 ;  table  of,  Table  IV, 
page  404. 

Velocity,  of  earth  in  its  orbit,  102, 
158;  of  light,  436;  of  moon's 
shadow,  203;  of  meteors  and 
shooting-stars,  317,  322;  of  star 
motions,  340,  341. 

Venus  (the  planet),  245-250;  phases 
of,  247 ;  transits  of,  250. 

Vernal  equinox,  the,  17,  36,  116. 

Vertical  circles,  11. 

VERY,  F.  W.,  measures  of  lunar 
heat,  150. 

Vesta,  the  fourth  asteroid,  260. 

Virgo,  56,  118. 

Visible  horizon  defined,  10. 

VOGEL,  H.  C.,  spectroscopic  deter- 
mination of  star  motions  in  the 
line  of  sight,  341 ;  spectroscopic 
observations  of  Algol,  Spica,  and 
Mizar,  360,  373,  374. 

Volcanoes  on  the  moon,  153. 

Vulcan,  the  hypothetical  intramer- 
curian  planet,  264. 

Vulpecula,  69. 

W 

Water  absent  from  the  moon,  148. 
Wave-length  of  a  light-ray  affected 
by  motion  in  the  line  of  sight, 


Doppler's    principle,     179,    341; 

affected  by  pressure,  179. 
Wave,  tidal,  its  course,  213. 
Way,  the  sun's,  342. 
Weather,  the  moon's  influence  on, 

151. 
Weight,  loss  of,  between  pole  and 

equator,  111. 
WILSON  and  GRAY,  temperature  of 

the  sun,  190. 

WOLF,    MAX,    introduces     photo- 
graphic   method    of    discovering- 

asteroids,  260. 
WOLF,  R.,  sun-spot  curve,  169. 


Year,  the  sidereal,  tropical,  and 
anomalistic,  127,  and  Table  I, 
page  401. 

Z 

Zenith,  the,  defined,  10. 

Zenith  distance  denned,  11. 

Zero  points  of  the  meridian  circle, 

418,  419. 
Zodiac,  the,  and  its  signs,  118;  its 

signs  as  affected  by  precession, 

126. 

Zodiacal  light,  the,  265. 
ZOLLNER,  J.  C.  F.,  determination 

of  planet's  albedoes,  242,  247, 253, 

268,  276,  281,  285;  measurement 

of  moonlight,   149;  measures  of 

light  of  stars,  348. 


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